Prep ingredients: Dice 1 medium yellow onion into small pieces. Mince 4 garlic cloves (about 1 tablespoon minced). Set aside.
Sear the chicken: Heat 1 tablespoon olive oil in a large skillet over medium-high heat for 1 minute until shimmering. Place 2.5 pounds chicken breasts in the hot oil and sear for 2 minutes on each side until golden-brown (the chicken does not need to be cooked through). This step adds depth of flavor. Transfer chicken to your crockpot.
Combine dry spices: In a small bowl, whisk together 2 tablespoons chili powder, 1 tablespoon cumin, 1 tablespoon paprika, 1 teaspoon dried oregano, 1 teaspoon salt, 0.5 teaspoon black pepper, and 0.5 teaspoon cayenne pepper. Set aside.
Layer ingredients: Add diced onion and minced garlic to the crockpot with the chicken. Open 1 can of diced tomatoes with green chiles (about 10 ounces) and pour into the crockpot. Spoon in 2 tablespoons tomato paste and the spice mixture. Pour 1 cup chicken broth over everything.
Stir to combine: Using a wooden spoon, stir all ingredients together until the chicken is fully coated with the tomato and spice mixture. The chicken should be mostly submerged in liquid (about 60–70% covered).
Checkpoint: You are ready to move on when all ingredients are combined, the chicken is arranged in the crockpot, and everything is evenly mixed.
Cook on low: Cover the crockpot with its lid. Set to LOW and cook for 6 to 8 hours. The chicken should be fork-tender and shred easily when fully cooked. If your kitchen is warm, check at 6 hours. If it is cool, it may need the full 8 hours.
Alternative quick cook: If you are short on time, cook on HIGH for 3 to 4 hours instead. The texture will be slightly less tender but still very good.
Checkpoint: You are ready to move on when you can easily pull a piece of chicken apart with a fork and it feels no resistance in the center.
Shred the chicken: Carefully remove the cooked chicken pieces from the crockpot using tongs or a slotted spoon. Place on a cutting board or in a shallow bowl. Using two forks (or a hand mixer on low speed with the paddle attachment), shred the chicken into bite-sized pieces. This takes 3–5 minutes by hand.
Return shredded chicken to sauce: Add the shredded chicken back to the crockpot and stir to combine with the sauce.
Add lime juice: Squeeze 2 tablespoons fresh lime juice (about 1 large lime) into the crockpot. Stir well to distribute. Set the crockpot to HIGH and cook uncovered for 15 minutes. This allows the lime to brighten the flavors and prevents the chicken from becoming mushy.
Checkpoint: You are ready to serve when the chicken is well combined with the sauce and the liquid is hot throughout (a quick stir should show steam rising).
Warm tortillas: While the crockpot finishes, warm 12–16 corn or flour tortillas. Stack them on a plate, cover with a damp paper towel, and microwave for 60–90 seconds until pliable. Alternatively, warm them one at a time in a dry skillet over medium heat for 30 seconds per side.
Assemble tacos: Place a warm tortilla in your palm or on a plate. Spoon 3–4 tablespoons of shredded chicken into the center. Add desired toppings: shredded cheddar cheese, sour cream, diced red onion, fresh cilantro, salsa, or lime wedges. Fold tortilla in half or leave open-faced depending on preference.
Serve immediately while the chicken is hot.