Boil salted water, cook pasta until al dente.
Season and cook chicken in olive oil until done, set aside.
Sauté bell peppers until soft.
Add garlic, cook until fragrant, then add cherry peppers.
Deglaze with red wine, reduce by half.
Add tomatoes, simmer for 5 minutes.
Stir in cream, simmer until thickened.
Cut chicken, add to sauce with pasta.
Adjust sauce with pasta water if needed.
Mix in Pecorino Romano, simmer briefly.
Garnish with basil, serve with cheese.