I was planning to put the chicken breast in the pan with butter and garlic and rosemary and cook it until it browns a bit I guess? I dunno, I also heard suggestions of putting it in the oven after a quick sear on the stove. Any tips? And what would be a good side dish to go with this?

Stick it in the oven to begin with. :)

I bake boneless chicken breasts about once a week. Lay 'em in the pan, sprinkle with seasoned salt, pepper, parsley, onion powder and minced garlic, bake at 350 for half an hour, at around 25 minutes rub a bit of barbecue sauce on 'em. I prefer PETA* brand.

* People Eating Tasty Animals:

http://www.galenacanning.com/products_pictures/petabbqsauce.jpg

If you're unsure of whether it's done, cut into the thickest part. If the juices run clear, it's safe to eat. Or you can use an instant read thermometer, making sure to get breast meat to 165 degrees F and leg/thigh meat to 175-180 degrees F.

Personally, I'd use an oven safe pan and brown the meat, then finish it in the oven (essentially a pan roast). It's a good way to insure that you're cooked all the way through if you're unsure about pan frying. Personally, I use cast iron, though that's simply because I have a beautiful 12 inch cast iron skillet that's a family heirloom and cooks wonderfully. Any good oven safe pan should do (i.e., stainless steel with a metal handle).

Good luck.

I like to grill them over chopped red savinas (they bleed out on them and the fiery juices sear themselves in to the striations of white meat). Anyway I just season them with mustard powder, sea salt, zest of lime and perhaps a few squeezes of lime. BBQ sauce is also a good one.