In a large skillet (I use my electric skillet) over medium-low heat, melt the butter. Salt and pepper the chicken breasts to taste. Place in the skillet and cook, covered, for 40 minutes.
In the meantime, prepare the rice according to package directions. Keep warm.
In a small saucepan, place chicken broth, brown sugar, spicy brown mustard and apricot preserves. Over medium heat, stir mixture often until heated through, about 4 or 5 minutes. Remove from heat and let stand until chicken is done. Sauce will thicken as it stands.
Spoon the sauce over the chicken and serve with the wild rice.