Heat olive oil in a large skillet over medium heat. Season the chicken breasts with salt, pepper, and oregano.
Add chicken to the skillet and cook for about 8 minutes per side, until golden brown and the internal temperature reaches 165°F. Remove from the skillet and set aside.
In the same skillet, melt the butter over medium heat. Add the garlic and cook until fragrant, about 1 minute.
Stir in the cherry tomatoes and season lightly with salt and pepper. Cook until the tomatoes begin to soften and burst.
Add the spinach and cook just until wilted.
Pour in the heavy cream and stir in the Parmesan cheese. Bring the sauce to a gentle simmer and cook for about 3 minutes, until slightly thickened.
Return the chicken to the skillet and simmer for 5 to 7 minutes, until heated through and coated in the sauce.
Serve Creamy Tuscan Chicken with lemon wedges on the side.