Heat olive oil over medium-high heat in a large skillet.
Season chicken breasts with oregano, salt, and pepper.
Add chicken breasts to the hot oil and cook until browned, about 5 to 6 minutes per side.
Remove chicken from skillet and set aside.
Melt butter in skillet; stir in garlic and cook for about 30 seconds, or until fragrant.
Pour in chicken broth or wine; stir and continue to cook until liquid has reduced, about 3 minutes.
Stir in artichokes; cook for 1 minute.
Add in baby spinach and cook for 1 more minute, or until spinach is wilted.
Stir in half-and-half and bring to a simmer.
Add mozzarella and parmesan; stir until combined.
Transfer chicken back into the skillet and cook for 5 more minutes, or until sauce has thickened and chicken is completely cooked through.
Remove from heat.