Slurp it into a hash? ;-)
#!/usr/bin/perl -w
use strict;
my %unique;
while (<DATA>) {
chomp;
$unique{$_} = '';
}
my @array = keys %unique;
$, ="\n";
print @array;
__DATA__
Brentwood
Brentwood
Westwood
Beverly Hills
Beverly Hills
Beverly Hills
Bev Hills Adj.
Palms
Mar Vista
Mar Vista
Mar Vista
Mar Vista
Mar Vista
Venice
Santa Monica
Santa Monica
LA/Crescent
LA/Crescent
Koreatown
3rd/LaBrea
3rd/LaBrea
3rd/LaBrea
(of course, if you want to preserve order too, some extra cunningness will be required; but the basic idea remains the same)