http://en.wikipedia.org/wiki/Unix_time#History explains a little about the origins of Unix time and the chosen epoch. The definition of unix time and the epoch date went through a couple of changes before stabilizing on what it is now.
But it does not say why exactly 1/1/1970 was chosen in the end.
Notable excerpts from the Wikipedia page:
The first edition Unix Programmer's Manual dated November 3, 1971 defines the Unix time as "the time since 00:00:00, Jan. 1, 1971, measured in sixtieths of a second".
Because of [the] limited range, the epoch was redefined more than once, before the rate was changed to 1 Hz and the epoch was set to its present value.
Several later problems, including the complexity of the present definition, result from Unix time having been defined gradually by usage rather than fully defined to start with.