I bought a ticket via Priceline and will be flying on 3 different airlines. Alaska from SEA to LAX, TACA from LAX to SJO then the return trip is TACA from SJO to LAX and US Air from LAX to SEA. I was assuming that I would be checking in with checked baggage on Alaska since that is the one I am taking first, but reading the fine print on my Priceline doc, it says

"One or more of your flights is listed as being “operated by” another carrier. In these cases, it is even more important to verify your check in location.When multiple airlines are included on a single ticket, the value of the ticket is held on what the airlines describe as the “ticketing carrier”. Your ticket value is held by US Airways."

So does that mean that I need to check in at US air instead?

No, you always check-in with the operating carrier. So, it is Alaska at SEA, and TACA on the way back at SJO.

If you run into problems and need to reschedule, rebook, etc, then you may need to contact USAirways.

Since they stress you must "...verify your check in location" I suggest you just call US Airways and ask them. I'm betting you'll check in with Alaska and I wouldn't want to give anyone else my luggage.