In a large skillet, heat olive oil over medium heat. Add the chopped onion and sauté until translucent, about 5 minutes. Add minced garlic and cook for an additional minute until fragrant.

In a small bowl, mix together chili powder, cumin, smoked paprika, oregano, salt, and black pepper. Sprinkle the spice mixture over the onions and garlic, stirring well to combine.

Add the chicken breasts to the skillet, followed by the chicken broth and diced tomatoes with green chilies. Bring to a simmer, then cover and reduce heat to low. Cook for 20-25 minutes, or until the chicken is cooked through and tender.

Remove the chicken from the skillet and shred it using two forks. Return the shredded chicken to the skillet, stirring to combine with the sauce. Allow it to simmer for an additional 5 minutes to absorb the flavors.

Warm the tortillas in a dry skillet or microwave. Assemble the tacos by placing a generous amount of pulled chicken on each tortilla, then top with shredded lettuce, diced tomatoes, cheese, and cilantro. Serve with lime wedges on the side.