I think you have a line seperator problem. DOS lines end with CR LF. Unix lines end with LF. If you're reading a DOS text file in unix, the chomp will remove the LF but leave the CR in, causing every line being printed to apear on top of each other. Try $/ = "\x0D\x0A"; before the read, or try adding $genome =~ s/\x0D//g; or try using the following:

#!/usr/bin/perl
use warnings;
use strict;
my $filename = 'T7.fa';
open(DNA, $filename);
my $genome;
{ local $/; $genome = <DNA>; }
close DNA;
$genome =~ s/\x0D\x0A//g;
print "$genome\n";
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