The sound of the organ trio--Hammond B-3, drums, and either sax or guitar out front--was a staple of Chicago jazz for years after the format emerged in the mid-50s. Sadly, there are exactly three such bands now appearing regularly in the city, and two of them feature the same organist, Chris Foreman. (While Chicago currently boasts several other top-notch organ players, none works in a traditional trio.) In Deep Blue, Foreman teams up with drummer Greg Rockingham and the brainy and soulful guitarist Bobby Broom; the partnership began in the early 90s, surviving long periods of inactivity before the group assumed a weekly slot at the Green Mill this spring. More than most organ trios playing today--such as those led by Larry Goldings and Sam Yahel--Deep Blue doesn't stray too far from the template laid down half a century ago. Much of this has to do with Foreman, a meat-and-potatoes player given to only occasional modernist flourishes: his strength lies in the way he builds a solo in texture and melodic complexity, chorus after chorus, until the organ becomes a shouting gospel choir. Behind him, Rockingham punches out crisp, bluesy beats and polished fills that also recall an earlier era of hard, unambiguous swing. But both men are able to follow Broom's lead when he opens things up, as he inevitably does. A veteran of touring bands led by Sonny Rollins, Kenny Garrett, and Dr. John, Broom draws from wide experience in a number of styles, and on recent discs under his own name he's excelled at turning old pop hits ("The Letter," "Layla," "Stand!") into new jazz standards. Broom has also fine-tuned his own improvising in recent years; once sprawling, his solos now feel more incisive and slyly energetic. Saturday, July 26, 8 PM, and Tuesdays, 9 PM, Green Mill, 4802 N. Broadway; 773-878-5552.