What is the best way to cook boneless skinless chicken breasts for chicken salad?

If they are large, I slice them horizontally to make them thinner so they will cook fast, marinate in a vinegary dressing and then I grill them. I did that for a bridal shower. Worked out great.

If you're starting from scratch, or making a special meal, you may want to pursue the holy grail of "best method."
But/and I always thought of chicken salad as one of those thrifty ways to (or was that Paul Simon, fifty ways to) use up all your un-beautiful but tasty and nutritious bits of chicken cooked simply for another meal, usually roasted.
So, she winds up, I say any method that gives you leftover chicken. And consider also using the dark meat - for flavor and kitchen economy (see Tamar Adler, Eugenia Bone and many other good writers).

For a really chic and mild chicken salad they should be poached - boned and skinless before going in. Roasting, pan broiling, rotisserie, with skin on and bone-in is always going to give a stronger taste to the chicken salad. The method used depends on audience. Keep your options open.

Either poaching it so its juicy and tender with flavorings, like a lemon grass and vanilla seed combo (trust me it's delicious!) in the poaching liquid OR grill it with a flavorful marinade like lemon and paprika or honey and mustard seeds then slice to serve. The juices from the pan can be deglazed with a mild white wine for example and used as part of the dressing

I bake them in Oarvhment paper and spritz them with olive oil. I cook them 50 minutes @ 350 in a convection oven. This method makes the best, moist chicken for chicken salad and you don't have to wash the pot with that nasty film in it. In a regular oven maybe 60 minutes.

fwiw, Ina Garten recommends roasting chicken breasts to be used in recipes. But she says to roast them skin on and on the bone, then discard the skin and bones afterward. You can find her recipe on the Food Network website.

I agree with Susan W. Poaching is the way to go. You could also poach it in the slow cooker if you're going to work. Then shred it right up.

I would say poaching and cooling it in the poaching liquid. You can even store it in the liquid if you aren't using it that day.