We always buy the cheapest boneless, skinless chicken breasts we can find, and they are never tough or chewy. The key is to avoid overcooking them, and to brine them for 3 - 5 hours for increased juiciness. Here is my brine recipe for 2 to 4 breasts:
1 T molasses
1/4 cup sugar
1/4 cup kosher salt
2 t garlic powder
2 t ground cayenne
2 t ground cumin
1/2 t ground black pepper
boil the molasses in 1 cup of water. Mix together the dry ingredients, and add to the boiling water. Continue boiling for 2 minutes, then let cool. Put chicken breasts in a large bowl, add the brine mixture, then add 4 - 6 cups water (or at least enough to cover the chicken). Refrigerate for 3 to 5 hours.
Remove breasts from brine, rinse and pat dry. Season with your favorite seasoning mix. (I use Kickin' Chicken). Grill over medium heat or hot coals for 4 - 5 minutes per side, depending on size of breasts.