(noun, slang.)
Zero; nothing: The search came up with zilch.
-- http://dictionary.reference.com
Zilch is an American slang term that fist appeared in the 1960s; the Oxford English Dictionary lists it as appearing in 1966, but it didn't come out of thin air. While some of its meaning probably comes from the fact that is sounds a little like nil and a little like zero, zilch was a null-set from the beginning.
In the 1920s college students came up with another nobody. There was John Doe, Thomas Atkins, John Nokes, and a big double-handful of others, but apparently the youngsters of the 1920s need one more; specifically, a German. Joe Zilsch was the new anti-hero, the nobody important, the whoever, the human metavariable. As far as we know, Zilsch was chosen just because it was a funny sounding foreign name1. Zilch is actually a more common surname than Zilsch, so the extra 's' may have been added for an extra bit of Germanishy feeling.
While 'Joe Zilsch' has since been judged to be too worthless to even symbolize nobody, he was fortunate enough to be plagiarized by the humor magazine Ballyhoo ("Now! All the crap in the world... At your finger tips!"), which in 1931 started using various Zilches (Henry P. Zilch, Otto Zilch) when it needed to plug a random name somewhere in its content. Ballyhoo was exactly what Americans needed to distract them from the Great Depression, and sales were exceedingly good. Eight years later sales weren't so good, and the magazine was discontinued.
Here we lose the trail. The 40s and 50s were slow years as far as zilch was concerned. But in the 60s zilch exploded onto the slang scene (hey, it's a groovy word!), and took on its current meaning. One half the 'the little man who wasn't there' and one half a portmanteau of 'zero' and 'nil'. By the late 70s it was appearing in mainstream dictionaries2.
Zilch is still a strong presence in the American language. It is often accompanied of other null words, because one nothing is never enough. ("Nada, zip3, zero, zilch!") Zilch also has heavy usage in the English English speaking world, showing that America has nothing to offer the UK.
Footnotes:
1. German organist Josef Zilch (1921) was born too late to be part of this etymology, but there may have been other famous Josef Zilches at an earlier date. Msg me if you find one.
2. It even appeared without the demeaning appellation of 'slang'. Even 'cool' was still slang in the 70s.
3. Zip, used to mean zero, predates zilch. It was used by students in the early 1900s to refer to a score of zero on a test.
References:
http://dictionary.reference.com/search?q=zilch&r=66
http://www.worldwidewords.org/qa/qa-zil1.htm
http://en.wikipedia.org/wiki/Ballyhoo_(magazine)