In a large skillet over medium heat, melt 2 tablespoons of butter. Add the minced garlic and sauté for about 1 minute until fragrant, being careful not to burn it.
Season the chicken breasts with salt, pepper, and dried oregano. Add the chicken to the skillet and cook for about 6-7 minutes on each side, or until the chicken is golden brown and cooked through. Remove the chicken from the skillet and set aside.
In the same skillet, add the remaining 2 tablespoons of butter, lemon juice, and lemon zest. Stir to combine and let it simmer for a minute.
Add the trimmed green beans to the skillet and drizzle with olive oil. Sauté for about 5-6 minutes until the green beans are tender but still crisp.
Return the chicken to the skillet, nestling it among the green beans. Cook for an additional 2-3 minutes to heat through and allow the flavors to meld.
Garnish with chopped fresh parsley before serving.