Add the sliced peppers and onion to the bottom of the slow cooker. Drizzle with olive oil.
Place the chicken breasts on top of the vegetables. You can slice them now or shred them later after cooking.
In a small bowl or jug, mix together the chopped tomatoes, tomato purée, lime juice, and all the spices. Stir well to combine.
Pour the sauce mixture evenly over the chicken and vegetables. No need to stir.
Cook on LOW for 5–6 hours or HIGH for 3–4 hours, until the chicken is cooked through and tender.
If using whole chicken breasts, remove and shred them with two forks. Return the shredded chicken to the slow cooker and stir to coat in the sauce.
Serve the fajita filling in warm tortillas with your favourite toppings such as grated cheese, sour cream, guacamole, salsa, or chopped fresh herbs.