Cook the gnocchi according to package instructions. Drain and set aside.
Heat olive oil in a large skillet over medium heat.
Season chicken breasts with salt and pepper, then add to the skillet. Cook until both sides are golden brown and cooked through, about 6-7 minutes on each side.
Remove chicken from the skillet and let rest before slicing into bite-sized pieces.
In the same skillet, add minced garlic and sauté for about 30 seconds, being careful not to burn it.
Add cherry tomatoes and cook until they begin to soften, about 3-4 minutes.
Pour in the chicken broth and dried oregano, stirring to combine. Simmer for 3-5 minutes.
Return the sliced chicken to the skillet, and fold in the cooked gnocchi. Toss gently to coat.
Sprinkle in grated Parmesan, stirring until melted and creamy. Adjust seasoning with salt and pepper if needed.
Serve immediately, garnished with fresh basil for a bright finish.