In a large nonstick skillet, heat the oil over medium heat until hot. Add the onion; sauté 5 minutes.
Sprinkle thyme and 1/4 teaspoon salt over the chicken. Add the chicken to the pan; sauté 6 minutes on each side or (less) until done. Remove the chicken from pan; keep warm.
Reduce the heat to medium. Add 1/4 teaspoon salt, jam, vinegar, and pepper to pan, stirring constantly until the jam melts. Spoon the sauce over the chicken and serve immediately.
I always pound out my chicken breasts a little bit to thin them out and even out their thickness. They cook up quicker and more evenly that way. Alternately, you can buy the thin-cut thicken cutlets and use those instead.
I love the sauce for this chicken, but the flavor might be overwhelming for kids. Serve a dish of the sauce on the side for the little ones- then they can dunk their chicken into the sauce if they wish.