Zilner Trenton Randolph (January 28, 1899, Dermott, Arkansas - February 2, 1994, Chicago) was an American jazz trumpeter and music educator.
Randolph attended Biddle University (now Johnson C. Smith University), the Kreuger Conservatory, and the Wisconsin Conservatory of Music, and played in territory bands including Bernie Young's (1927-31). He moved to Chicago in 1931 and became Louis Armstrong's musical director in 1931-32 and again in 1933 and 1935. Randolph also played trumpet on a number of Armstrong's recordings and composed the tune "Old Man Mose". He played with Carroll Dickerson and Dave Peyton in the middle of the decade, and led his own Chicago band later in the 1930s. He arranged for such bandleaders as Earl Hines, Woody Herman, Fletcher Henderson, and Duke Ellington, and led a quartet in the 1940s. He never recorded a session as a leader.
After the 1940s Randolph devoted himself mainly to teaching, but recorded as a pianist in 1951 and led the house band at the Indiana Theater off and on during the 1950s.
Zilner's son Lucious Randolph played trumpet with Sun Ra and Jerry Butler, among others. His daughter Hattie recorded for the small Chicago label Drexel in 1955 and sang with Sun Ra from 1957 to 1959.