Pat chicken dry, season with salt and pepper, then sear in 2 tablespoons olive oil over medium-high heat until golden (about 4 minutes per side); transfer to plate.
Toss green beans with remaining 1 tablespoon olive oil and salt; spread on a baking sheet and roast at 425°F for 12 minutes.
In the same skillet, mince garlic and cook 30 seconds in butter, then add tomatoes with chiles and smoked paprika; simmer 2 minutes.
Return chicken to skillet and simmer in sauce for 2 minutes until internal temperature reaches 165°F.
Divide chicken, sauce, and green beans onto four plates and serve immediately.