Charles "Chuck" Riggs was born in Westerly, Rhode Island, on August 5, 1951, and started on drums at ten. His apprenticeship was in rhythm and blues bands rather than jazz ones, and he came to jazz essentially self-taught, with only a short spell of formal study at a music school in his home state. The turn came in 1972, when he joined the Hamilton-Bates Blue Flames, a Providence blues-and-jazz group built around guitarist Fred Bates and a young harmonica player and alto saxophonist named Scott Hamilton, with Preston Hubbard on bass. Hamilton switched to tenor saxophone, the band's centre of gravity moved from blues to swing, and the Blue Flames turned into the Scott Hamilton Quartet. That is the group Riggs spent the next two decades in.

In 1976 he moved to New York City, and both his own account and AllMusic's entry give the same reason: Roy Eldridge asked him to. Concord Jazz had signed Hamilton the year before, but Concord's California sessions used its house drummer Jake Hanna, so Riggs does not appear on Hamilton's first three albums. His recording career starts instead with the New York band: Scott Hamilton and Warren Vaché With Scott's Band in New York City, taped at Soundmixers in Manhattan and issued as Concord CJ-70 in 1978, with Chris Flory on guitar, Phil Flanigan on bass and Norman Simmons on piano. The distinction matters, because it holds for the whole Concord run. When Hamilton recorded in California or in London, the drum chair went to Hanna, Jeff Hamilton, Connie Kay, Allan Ganley, Roy McCurdy or Lewis Nash. When he recorded in New York with his own working band, it went to Riggs. Back to Back with Buddy Tate followed in 1979, Skyscrapers was cut at Soundmixers in July of that year with Warren Vaché, Joe Temperley, Harold Ashby and George Masso added, and in October 1979 the group played the Jazz Jamboree festival in Warsaw, two of its numbers surviving on a Polskie Nagrania Muza LP.

The other bandleader who claimed him in these years was Bob Wilber. Riggs is on Dizzyfingers, recorded August 24, 1980 for Wilber's own Bodeswell label with Mark Shane on piano and Lars Erstrand on vibraphone, and on Bob Wilber and the Bechet Legacy, taped on location at the club Bechet's in New York on January 22, 1981. The Bechet Legacy toured: Michael Steinman has published film of the band at the Bern Jazz Festival in Switzerland in the spring of 1984, with Wilber, Randy Sandke, Shane, Mike Peters, Len Skeat, Riggs and the singer Joanne "Pug" Horton, introduced from the stage by Clark Terry. Wilber's period expertise is also why Riggs turns up in a film credit. When Francis Ford Coppola made The Cotton Club (1984), Wilber transcribed and conducted the Ellington and Calloway numbers, and the band he put together for the soundtrack sessions had Riggs on drums, Shane on piano, John Goldsby on bass and Peters on guitar and banjo. Riggs also worked with the World's Greatest Jazz Band and, in both big-band and small-group settings, with Benny Goodman.

The Hamilton quintet with John Bunch, Flory and Flanigan was the constant through the 1980s, and it recorded steadily: Close Up (Soundmixers, February 1982), In Concert, taped live at Yamaha Hall in Tokyo in June 1983, The Second Set from the same Tokyo engagement, The Right Time (Penny Lane Studios, January 1986) and Plays Ballads (New York, March 1989). The same rhythm section backed the guests Concord kept sending, so Riggs is on Ruby Braff's A First (Penny Lane, February 1985) and A Sailboat in the Moonlight, on Maxine Sullivan's Uptown (January 1985) and Swingin' Sweet, on Flip Phillips's A Sound Investment (1987) and on a Bunch trio date, The Best Thing for You (1987). WKCR broadcast the Braff quintet live from the West End Cafe in New York on March 29, 1985, Phil Schaap announcing. Away from Hamilton he made Easy Going with the Warren Vaché Sextette (Penny Lane, December 1986) and Duke Robillard's Swing (Rounder, 1987), and he was aboard the S/S Norway in October 1986 for the Fourth Annual Floating Jazz Festival, where Flip Phillips's The Claw was taped with Al Cohn, Buddy Tate, Hamilton and Clark Terry.

He was also the third of a working trio: Kenny Davern's clarinet and Dick Wellstood's piano, with Riggs the only other instrument. That group left two co-billed records, Live Hot Jazz, recorded at the Maryland Inn in Annapolis and issued on Statiras with a David Stone Martin cover and liner notes by Dan Morgenstern, and Stretchin' Out, cut on December 18, 1983 and issued on Jazzology. In the early 1990s he was in the Concord All-Stars, the label's touring house band, cutting Concord All-Stars on Cape Cod in Hyannis, Massachusetts on May 3, 1992 with Dave McKenna, Gray Sargent, Marshall Wood, Hamilton and the singer Carol Sloane. The rest of that decade ran through Chris Flory's leader dates for Concord, Marty Grosz's two boisterous small-band records, Jon-Erik Kellso's Arbors debut Chapter I (1993, with Milt Hinton, Scott Robinson, Jeremy Kahn and Frank Vignola), the two-volume Billy Strayhorn project the Keith Ingham-Harry Allen Quintet recorded on March 12 to 14, 1993, and a Bob Wilber Jazz Repertory Ensemble recreation of King Oliver's Creole Jazz Band made for the Smithsonian Institution. Hamilton's Blues, Bop & Ballads, cut at Sony Music Studios on February 23 and 24, 1999 with Robillard on guitar, is the last of the Concord albums.

From 2003 the centre of his week shifted to Harry Allen, and it stayed there for a decade. Allen used him on the self-released The Harry Allen Quartet (Nola Studios, April 21 and 22, 2003) with Joel Forbes and Joe Cohn, and that quartet then made four Arbors albums, from Hey, Look Me Over (2004) through Plays Music from South Pacific (2009), plus a run of Japanese releases for Swingbros. When Rossano Sportiello replaced the guitar with piano, the resulting Allen-Sportiello-Forbes-Riggs quartet recorded for Challenge in the Netherlands: Hits By Brits (2007), New York State of Mind (February 2009), Rhythm on the River (2011) and 'Round Midnight (February 2012, with Hamilton added). The same four backed Rebecca Kilgore on Live at Feinstein's at Loews Regency and The Sound of Music, and played Allen's Monday-night residency at Feinstein's through 2011 and 2012. The SmallsLIVE archive lists thirty-one dated nights for him between September 25, 2007 and February 13, 2013, mostly with Allen's quartet and Flory's trio, plus dates with Sportiello and the Steve Ash Trio. The last two of those nights, February 12 and 13, 2013, were recorded and released as Scott Hamilton's Live at Smalls, with Sportiello, Hassan Shakur and Riggs, who is credited as one of its producers. It closes a working relationship with Hamilton that had run for forty-one years. No later recording, performance or death notice for him has been published.

Riggs named his own models, and the list is a map of where he sits: Sid Catlett, Jo Jones, Dave Tough and Jake Hanna from the swing lineage, Connie Kay from the Modern Jazz Quartet, and Jimmy Cobb and Philly Joe Jones from hard bop. What he took from the first group is what people hear. AllMusic's entry calls him a thoughtful, listening drummer who plays with subtlety and swing, and the settings he spent his career in demanded exactly that: a saxophone or cornet, a piano, a guitar and a bass, small rooms, standards and Ellington, and a drummer whose job was to keep the tempo honest and stay out of the front line's way. He almost never soloed on record. Nat Hentoff, writing the notes for The Right Time, framed the band around Hamilton's insistence that his colleagues also had something to say; the point of the Hamilton-Bunch-Flory-Flanigan-Riggs quintet was that it functioned as one machine across a decade of albums, and Riggs is the reason it never rushed. The bop influences show up mostly in the harder company he kept later, the Ehud Asherie and Joe Cohn quintet dates, where the same approach works unchanged. Nothing in his playing belongs to a revival: he learned the idiom in an R&B band and then from the men who invented it, several of whom, Goodman, Braff, Tate, Wellstood, Phillips, he ended up working for.