use warnings;
use strict;

open my $first, "<", "first.txt" || die "first.txt: $!\n";
# three-argument form of open is safer
# scalar variables as filehandles are more modern than barewords
open my $second, "<", "second.txt" || die "second.txt: $!\n";
while (! eof $first && ! eof $second) { # while both filehandles can be read
 chomp (my $fline = <$first>);
 # you can read the line and chomp at the same line
 chomp (my $sline = <$second>);
 print "${fline},${sline}\n";
}
close $first;
close $second;