Season chicken with salt and pepper. Heat oil in a large skillet over medium-high heat. Sear chicken 4 to 5 minutes per side until golden; transfer to a plate.

Reduce heat to medium. Add onion and cook 3 to 4 minutes until soft. Stir in garlic and cook 30 seconds. Sprinkle flour over onions and stir constantly for 1 minute.

Gradually whisk in broth, scraping up any browned bits. Bring to a simmer, return chicken and juices to the skillet, cover, and cook 10 to 12 minutes until chicken reaches 165°F.

Transfer chicken to a cutting board and shred with two forks. Return shredded chicken to the skillet, stir in butter if using, and serve hot over your choice of side.