Preheat a medium to large skillet over medium-high heat, for about 1 minute or until the surface of the pan is hot. Add the oil and heat until rippling on the surface. Pat the chicken breast dry and season with salt and pepper.
Place the chicken in the pan and cook until the meat is golden, about 4 minutes. Turn the chicken breasts, lower the heat to medium and add 1 tablespoon of the butter. Cook until firm to the touch or an instant-read thermometer registers 160 degrees F, about 4 to 6 minutes more. Transfer the chicken to a plate to rest.
Pour off any fat remaining in the skillet. Add the vinegar and deglaze over medium-high heat, scraping up any browned bits stuck to the bottom of the pan with a wooden spoon. Add the cider and the broth. Bring to a boil and cook until it thickens to form a sauce, about 6 minutes. Whisk in the remaining 2 tablespoons butter, lemon juice and thyme leaves. Return the chicken to the pan, adjust the seasoning with salt and pepper, and serve.