Cook the angel hair pasta according to package instructions until al dente; drain and keep warm.
In a large saucepan over medium heat, melt the butter with the olive oil.
Season the chicken pieces with salt, pepper, dried oregano, and Italian seasoning.
Add the seasoned chicken to the saucepan and cook until almost cooked through, about 4–6 minutes depending on size.
Add the sliced mushrooms and minced garlic to the pan with the chicken and cook until the chicken is fully cooked and mushrooms are softened, about 3–4 minutes.
Stir in the sliced black olives, the entire can of diced tomatoes with juices, and the spinach; cook, stirring often, until the spinach wilts, about 3–4 minutes.
Reduce heat to medium-low and stir in the half and half; simmer just until heated through and slightly thickened, about 2 minutes, then remove from heat.
Add the drained pasta to the sauce and toss gently until combined and coated. Serve immediately.
