Pat chicken dry, season with salt and pepper, then dredge in flour.
Heat olive oil and 1 tablespoon butter in a skillet over medium-high heat. Sear chicken 4–5 minutes per side until golden and cooked through. Set aside.
Lower heat to medium. Add remaining butter and garlic; cook 30 seconds until fragrant.
Add broth, lemon juice, lemon zest, and oregano. Scrape up browned bits.
Simmer 4–5 minutes until slightly thickened.
Return chicken to skillet, spoon sauce over top, and cook 2 more minutes.
Garnish with parsley and serve.