Don't open and close the file over and over again. Take advantage of the fact that your file is sorted.

my $fh;
my $last;
while (<>) {
   my ($file) = /^([^,]+),/;
   if (!defined($last) || $file ne $last) {
      open($fh, '>', "$file.txt")
         or die($!);
   }
   print $fh $_;
   $last = $file;
}
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