On a rainy evening in August of last year, a barely advertised show by the Chicago-based drummer and beatsmith Makaya McCraven jammed an overflow crowd into H0L0, a sparse little basement club in Ridgewood, Queens. His band was a group of New York musicians, some of whom Mr. McCraven had hardly played with before; what they performed was entirely improvised, but with Mr. McCraven subtly steering, listeners had room to get comfortable, to fall into the music. His thick snare drum splattered against the bulb tones of Joel Ross’s vibraphone patterns, making an elliptical groove. Sometimes Brandee Younger’s plucks on the harp led Mr. McCraven into a buoyant, driving beat. Elsewhere, he minimized himself, letting Dezron Douglas’s bass guide the rhythm.

Like many of Mr. McCraven’s shows, the night was recorded, providing raw material for “Universal Beings,” an album he released in October to wide acclaim. Since his second record, “In the Moment,” in 2015, Mr. McCraven has put out a string of albums and mixtapes that amount to a proof of concept. Each one features crudely recorded live improvisations that he has sliced up, pared down and spritzed with effects and extra instrumentals. Part concert bootleg, part hip-hop mixtape, his music — borne of a process rather than a compositional method — has the potential to open up the way musicians think about improvisation.

“Something that I feel is severely missing in jazz is a connection to the aural tradition — it not just being on the page,” Mr. McCraven said in a phone interview this week.

His ability to wrap his albums in the dark allure of a club show, the timeless texture of an old Folkways record and the sonic layering of a hip-hop producer has turned Mr. McCraven, 35, into the most discussed young musician on a Chicago jazz scene teeming with fresh energy. “In the Moment” was just the second release on International Anthem, a jazz-and-more label that has since become a clearinghouse for innovative Chicago music. “Universal Beings” — a double album culled from live performances in four cities, each featuring prominent young local musicians — is the label’s first release to turn a real profit.