"nothing," 1957; "insignificant person," 1933, from use of Zilch as a generic comical-sounding surname for an insignificant person (especially Joe Zilch). There was a Mr. Zilch (1931), comic character in the magazine "Ballyhoo," and the use perhaps originated c. 1922 in U.S. college or theater slang. Probably a nonsense syllable, suggestive of the end of the alphabet, but Zilch is an actual German surname of Slavic origin.
The [Cadence] agency aims to have each album cover actually promote the record, on the theory that "the day of pretty, boffy, zoomy and zingy covers for the sake of zilch is no more." [Billboard, Oct. 28, 1957]