Place chicken breasts in the crock pot. In a separate bowl combine diced tomatoes (including liquid), chillies, garlic, chicken broth, cumin, and salt. Mix together and pour over chicken.
Cook on low 5-5 1/2 hours, or until chicken is cooked. Remove chicken from the crock pot and shred with two forks; place back in the crock pot.
Add half and half or heavy cream and stir. Allow to simmer for 15 minutes before serving. Taste it and add more salt and cumin if necessary, to taste.
Serve with tortilla chip strips or crushed tortilla chips, cheese, cilantro, and a squeeze of lime. Enjoy!