If you want to read a specific number of bytes without regarding to the actual characters, sysread will fit the bill. Something like this should work:

open IN, "hugefile.txt"
    or die "Can't open huge file: $!\n";
open OUT, ">biggerfile.txt"
    or die "Can't open bigger file: $!\n";
my $line;
while (sysread(IN, $line,  150))
{
    print OUT "$line\n";
}
close IN;
close OUT;
[download]

(Warning, I haven't tested this.)

More info on sysread available here and here.

Update
Look at I0's and jlongino's answers in this thread. They're better answers than mine!