Something similar to this should do it. The trick is not to update $lastline until you don't have a match. As a side note, in the past I have successfully loaded around 100K lines into an array. You may be surprised at what Perl can handle.

open (IN, "$input_file");
open (OUT, ">$output_file");

my $lastline = <IN>;
print OUT $lastline;
while(<IN>){
    my $line = $_;
    if ($line eq $lastline){
        next;
    }
    print OUT $line;
    $lastline = $line;
}
[download]

update: corrected typo