Season the chicken with salt, pepper, and Italian seasoning.
Heat olive oil and 1 tablespoon of butter in a large skillet over medium-high heat. Add the chicken and cook for 5-6 minutes per side until golden brown and cooked through. Remove and set aside.
In the same skillet, melt the remaining 2 tablespoons of butter. Add the minced garlic and red chili flakes, cooking for 1 minute until fragrant.
Add the trimmed green beans and chicken broth. Cook for 4-5 minutes until the beans are tender-crisp.
Stir in the lemon juice and lemon zest. Return the chicken to the skillet, tossing everything to coat in the pan sauce. Serve immediately.