bobj1, welcome to FlyerTalk I hope you find these boards informative and enjoyable.

CKS (Chiang Kai Shek) airport is reasonably compact, and it takes just a couple of minutes to go from Terminal 1 to 2 via shuttle. I have to admit that I've never done that directly, as I've only used Terminal 1, but I've driven from and two the airport dozens of times, watching Terminal 2 as it was being constructed, and have never seen any congestion on the airport roads linking the terminals.

As far as luggage goes, I assume that you will be transiting CKS, and will check your luggage through from LAX to BKK. In order to get you luggage, you'd have to clear immigration in Terminal 2, get your luggage, go through customs, drag your luggage to Terminal 1, check your luggage, clear immigration.... you get the picture. It's unlikely you'd make it in an hour. If you just transit from 2 to 1, you should be at the gate in Terminal 1 about 15 minutes after you disembark at Terminal 2.

What class are you flying in EVA. I ask because EVA has an additional class between economy and business, called Evergreen Deluxe, which is a great value. If you are in AA business or above, you're all set, but if you're in coach, it would be nice to consider Deluxe, which is basically business class seats with coach service. However, I don't know how/if an AA/EVA code-share in economy could be upgraded to Deluxe.

Please let us know how your trip to BKK went.