OK, this is probably not the most beautiful and compact regex, but it works:

my $string = "New York/Chicago/New York/Chicago/Boston";

1 while $string =~ s!(^|/)([^/]+)(.*)/\2(/|$)!$1$2$3$4!g;

print $string;
#outputs "New York/Chicago/Boston"
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Update Well of course this is an abuse of regex. I would not use it myself nor recommend it, but it's a nice exercise.