New kitten chasing Adult cat. Advice?

We just got our kitten that we have been waiting a couple months for, she is about 12-13 weeks, She just got here tonight and she is chasing the older male cat around(he's a little over a year old), the male cat is making little noises but no hissing is involved, Could this just be playing or is this a power struggle. the kitten likes to puff up a little but the male cat doesn't puff up at all.

If the new one just got there, she should not even be with your other cat yet!  Introductions are supposed to be slow and controlled.  She is probably just trying to play, but your other cat hasn't had time to adjust.  Cats are not like dogs and introductions should not just be sudden.  There are many articles about how to introduce cats.  Here is one from the ASPCA and another from Pam Johnson-Bennett.  Try backing up and re-introducing them the slow way and both will be happier.

http://www.aspca.org/pet-care/virtual-pet-behaviorist/cat-behavior/introducing-your-cat-new-cat

http://www.catbehaviorassociates.com/how-to-introduce-a-second-cat/

I feel bad because I just added the two new cats without doing it slowly. However both my older cats were fine after a day. It could of gone real wrong though.

We have an article on the topic here as well - 

http://www.thecatsite.com/a/introducing-cats-to-cats

@Evan1991  Congratulations  on your new cat! Sounds like you have a very tolerant older cat there, so hopefully you got lucky with the unplanned introduction there. As long as the older cat isn't hissing or expressing aggression towards the kitten, it should be safe to proceed. One word of advice though, if you feel things are getting a bit too aggressive make sure you monitor your own reaction and that of the other humans around. Sometimes people react instinctively by shouting at the cats thus adding more tension into an already tense situation, which could result in more aggressive behavior in the future.