Pour the olive oil into the bottom of the slow cooker and spread it to coat the surface lightly.
Place the chicken breasts in a single layer over the oil.
Scatter the sliced bell peppers, onion, and minced garlic evenly over the chicken.
In a bowl, stir together the diced tomatoes with their juice, chicken broth, Italian seasoning, salt, and black pepper.
Pour the tomato mixture over the vegetables and chicken, making sure the liquid reaches the bottom of the pot.
Cover and cook on low until the chicken reaches an internal temperature of 165°F and the vegetables are soft.
Serve the chicken breasts with the sauce and vegetables spooned on top.