I went with

next if ($chromosome =~ "chrM");

Also note that  $chromosome =~ "chrM" matches if  "chrM" is found anywhere in the  $chromosome string:

c:\@Work\Perl\monks>perl -wMstrict -le
"my $chromosome = 'foo xx chrM yy bar';
 print 'found a chrM' if $chromosome =~ 'chrM';
"
found a chrM
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This is because you no longer anchor the match to the start of the string (as you do in the code in the OP) with the  ^ match anchor regex operator. The match  /^chrM/ would IMHO be better for what you seem to want.

Another point is that the data posted in the OP has a leading space or spaces in some cases. Leading whitespace will cause the  /^chrM/ match to fail. If leading whitespace may be present in real data, I would recommend something along the lines of  /^\s*chrM/ instead.