When connecting from UA (from SFO) to AA (going to Montreal -- YUL) at ORD, does one have to go outside security?

I don't believe you have to if you are careful, and WALK, don't take the train between the terminals. I know you can walk between T-1 and T-2, and think you can between 2 and 3 airside. Make sure you don't go past security. Just keep going right.

You can walk between the terminals 1, 2 and 3. Just follow the signs and be careful - in a couple of places you may leave a secure area by mistake and have to process through security again.