Heat oil in a heavy-bottomed skillet over medium-high heat.
Season chicken breasts with salt and pepper. Brown chicken on both sides, about 3 minutes per side. Remove chicken to a plate and keep warm.
Add apples and shallots to the skillet. Cook until apples begin to soften, about 2 minutes. Add thyme, salt and a generous grinding of black pepper. Cook 1 minute. Pour in chicken broth and cider and cook over high heat until the liquid has reduced by half, about 5 minutes.
Return chicken breasts to the skillet, nestling them in among the apples. Reduce heat to medium-low and simmer until chicken is no longer pink in the middle, about 8 minutes.