Pianist Jimmy Walker, at 84, is probably Chicago’s oldest working bluesman. His musical tenure here goes back at least to the late 20s, when he accompanied guitarist Lonnie Johnson and others at private parties and dances; a few years later he was working places like the Square Deal Club on Division Street, sometimes accompanied by guitarist Homesick James. As befits an elder statesman, Walker has developed a style over the years that’s dignified, gentle-rolling, and tasteful. His understated bass work supports a light, almost delicate touch on the treble keys, punctuated by an occasional brilliant flurry or boogie-woogie break. That lightness can be deceptive, however; Walker’s playing provides a rock-solid foundation for his vocals and the musical excursions of the band. It’s that timeless combination of straight ahead musicianship and good taste that’s becoming all too rare as veterans like Walker drift farther into semiretirement. Tuesday, B.L.U.E.S, 2519 N. Halsted; 528-1012.