Heat oven to 400°. Spray a baking dish with nonstick cooking spray.
Whisk together the apricot preserves, ketchup, mustard and ginger. Reserve 1/4 cup of the mixture.
Place chicken in the prepared baking dish and spread the remaining apricot mixture over the top. Bake at 400° for 20 to 25 minutes or until internal temperature reaches 160° on an instant-read thermometer.
Make rice following package directions, using the olive oil.
To serve, sprinkle the hazelnuts over the chicken breasts and stir the reserved apricot mixture into the cooked rice.