Looks a little over-engineered to me. So here's a version I knocked together

use strict;
use warnings;

@ARGV == 2 or die("Usage: $0 FILE PARTS\n");
my($file,$partsize) = @ARGV;

my $filesize = -s $file or die("ack: $!");
my $div = $filesize / $partsize;

my $cnt = 0;
open(my $fh, $file) or die("ack: $!");
{
  local $/ = \$div;
  while($filesize > 0) {
    open(my $chunk, ">${file}.chunk$cnt") or die("ack: $!");
    print $chunk scalar <$fh>;
    $filesize -= $div;
    $cnt++;
  }
}
[download]

Not sure if it works perfectly everytime, but it should achieve roughly what you want (otherwise, tweak at will ;).
HTH

_________
broquaint