Place the chicken breasts in the bottom of the slow cooker. Add the diced poblano peppers, chopped onion, and minced garlic on top.
Pour the can of fire-roasted tomatoes and the frozen corn over the vegetables. Sprinkle the cumin, chili powder, oregano, salt, and black pepper evenly across the top.
Pour the chicken broth over everything. Do not stir yet.
Cover and cook on low for 6 hours or on high for 3 hours, until the chicken is fully cooked and shreds easily.
Remove the chicken breasts, shred them with two forks, and return the shredded chicken to the slow cooker. Stir to combine all ingredients.
Ladle into bowls and top with chopped cilantro. Serve with lime wedges on the side.