Heat oil in a large nonstick skillet over medium-high heat. Sprinkle chicken with salt, thyme, and pepper. Add chicken to pan; cook 5 minutes on each side or until done. Remove chicken from pan; keep warm.
Add cider to pan, scraping pan to loosen browned bits. Reduce heat to medium-low; cook until reduced to 1/3 cup (about 5 minutes).
Add sliced apple and half-and-half; simmer over low heat 10 minutes or until sauce thickens and apples are tender, stirring occasionally. Serve sauce with chicken immediately.