Pat the chicken breasts dry with paper towels. Season both sides evenly with salt and black pepper.
Heat olive oil in a large skillet over medium-high heat until shimmering.
Add the chicken breasts to the skillet and cook for 5-6 minutes on each side, or until golden brown and cooked through (internal temperature should reach 165°F). Remove chicken from the skillet and set aside on a plate.
Reduce heat to medium. Add minced garlic to the skillet and sauté for 30 seconds until fragrant, stirring constantly to prevent burning.
Pour in the chicken broth, lemon juice, lemon zest, and dried oregano. Stir to combine and bring the sauce to a simmer.
Let the sauce simmer for 3-4 minutes until it slightly reduces.
Add the fresh spinach to the skillet, stirring it into the lemon sauce. Cook for 2-3 minutes until the spinach wilts.
Return the cooked chicken breasts to the skillet, nestling them into the spinach and sauce.
Add the butter to the skillet and stir gently until melted and incorporated into the sauce.
Cook everything together for an additional 2 minutes to warm through and allow the flavors to meld.
Serve the chicken topped with the lemon spinach sauce immediately.