I'm changing my road bike chain, and for the life of me, I can't get the darn KMC missing link to lock together.

I looks so easy on this video:
http://www.youtube.com/watch?v=Lkqsv...eature=related

but on my chain, the missing link pieces only fit when there's no chain between them. The moment I put the chain in, it seems that the link doesn't quite fit, and I can't "lock" it. Anybody have a suggestion? (It's a brand new chain.)