Heat a large skillet over medium heat. Add the olive oil and half of the butter. Let it melt.
Season the chicken with salt and pepper on both sides. Add it to the pan and leave it alone for a few minutes so it can brown.
Flip the chicken once it releases easily. Add the remaining butter and the garlic. Stir the garlic around briefly so it does not burn.
When the chicken is almost cooked through, push it to one side of the pan. Add the green beans to the empty space and season lightly.
Cook the green beans, stirring occasionally, until they are bright and tender but not soft.
Stir everything together in the pan. Taste and adjust salt or pepper if needed.
Remove from heat. Add red pepper flakes or a squeeze of lemon if using. Let it sit for a minute, then serve.
