I was going to suggest poaching them. But Niknud's suggestion of steaming will work also. I still violently dislike boneless, skinless chicken breasts because you are throwing away everything that gives them flavor.
You could also try roasting them ahead---with skin and bone---and stripping off the meat and adding that to finish your stir fry.
Whenever I do stir fry with boneless, skinless chicken breasts, I always steam the chicken first. Mostly because I've had the same problem as you with toughness. It takes a little bit more time, but nothing is more tender than a steamed chicken. Put a little sake or mirin and a sampling of whatever spices you will use in the final dish in with the steaming water and you get bonus flavor! You can even do it the day before and then just shread it and toss it in your wok (or saute pan like me) and give it a good coating of your flavors.
I find that if I cut them in cubes, they turn out stringy; in strips, crosswise, not so much. I also second rachelib's suggestion to coat them in egg white and cornstarch!
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You could also try roasting them ahead---with skin and bone---and stripping off the meat and adding that to finish your stir fry.