Lightly spray the bottom and sides of a 10-inch casserole dish (or any baking dish large enough to hold the chicken pieces). Place the chicken breasts in the coated baking pan.
With a wooden spoon, mix the mustard, honey, apricot preserves, and ginger in a small mixing bowl until well blended. Brush (or spoon) the mustard mixture over the tops of the chicken breasts. Bake the chicken, uncovered, for 30-45 minutes (depending on thickness of the breasts).
After 15 minutes of baking turn over each chicken breast, spoon sauce over them, and continue baking for the remaining 15 minutes, or until breasts are thoroughly cooked.
Transfer the chicken breasts to individual plates. Spoon the sauce over each serving.
For my kids, I like to put their portion of the sauce in a condiment cup so they can use it as a dipping sauce. (What can I say--it's a kid thing.)