Obviously, Perl thinks that what is in $cychpTxtFile does not point to a valid filename.

There are two easy ways for this to happen:

• There is whitespace at the end of the filename.
  Print $cychpTxtFile within two delimiters to see whether that is so: print "[$cychpTxtFile]" for example.
• There is no drive letter at the start of your filenames. If you are under Windows (as the upper case filenames suggest), did your script maybe change the current drive from C: to something else?
  If you are running under OSX, did you maybe mount an HFS volume under an HFS+ tree?

If these suggestions yield nothing, you will have to show us how you populate $chunked{$keySets}. Also, why are you so certain that the .txt files exist in that location?

On the shell, does</c>

ls "/Users/.../Desktop/cychip/cyto/Oligo/Oligo 2012/eggs/010613ESA ABN
+. CONTROL_(CytoScanHD_Array)_2012.cyhd.cychp.txt"
[download]

or

dir "\Users\...\Desktop\cychip\cyto\Oligo\Oligo 2012\eggs\010613ESA AB
+N. CONTROL_(CytoScanHD_Array)_2012.cyhd.cychp.txt"
[download]

find the files?

Update: I'm wrong and boftx hits the nail on the head. You're using Parallel::ForkManager, and that means that the changes in the child (the push) do not propagate back to the parent. See perlipc for various ways of communicating the information back to the parent.