You could also try a much simpler method, involving PerlIO::gzip:

#!/usr/bin/perl

use strict;
use warnings;
use PerlIO::gzip;

my $Usage = "Usage: $0 filename-to-compress\n";
die $Usage unless ( @ARGV == 1 and -f $ARGV[0] );

open( IN, "<", $ARGV[0] ) or die "$ARGV[0]: $!\n";
open( GZIP, ">:gzip", "$ARGV[0].gz" ) or die "$ARGV[0].gz: $!\n";

$/ = undef;
$_ = <IN>;
print GZIP;
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If you want to use this on an input file that is too big to fit in memory all at once, just use the normal I/O idiom with a while loop -- the result will be the same:

# $/ = undef;
# leave $/ at it's default value...

while (<IN>) {
    print GZIP;
}
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UPDATE: (2010-10-18) It seems that PerlIO::gzip should be viewed as superseded by PerlIO::via:gzip. (see PerlIO::gzip or PerlIO::via::gzip).