Add the chicken breasts to the slow cooker. Top with the diced onion, minced garlic, diced zucchinis, and the can of tomatoes with green chilies.
Sprinkle the chili powder, cumin, and salt over the ingredients. Pour the chicken broth around the edges.
Cover and cook on low for 6 hours or high for 3 to 4 hours until the chicken reaches an internal temperature of 165°F and shreds easily.
Remove the chicken to a cutting board and shred it with two forks. Return the shredded chicken to the slow cooker and stir everything together.
Spoon the chili into bowls and top each serving with shredded cheddar cheese. Add chopped cilantro if desired.