In a large mixing bowl, add the chicken, taco seasoning, 1 tablespoon oil, and lime juice. Thoroughly mix and set aside.
Heat up 1 tablespoon oil in a large pan or skillet over medium-high heat and cook chicken slices for 4-5 minutes per side. Transfer to a plate and set aside to rest for 5-10 minutes. Once cool enough to handle, use a fork to shred the chicken into small pieces.
Under medium-high heat, add remaining tablespoon of oil in the same skillet used to cook the chicken, add in the onions, peppers and garlic. Season with salt and pepper to taste and sauté until veggies starts to soften, 6-8 minutes.
Mix in the diced or crushed tomatoes and chicken broth. Give sauce a taste and season with salt and pepper as needed before mixing in the shredded chicken.
Reduce heat to low and simmer shredded chicken mixture for 10-15 minutes to allow the flavors in the sauce to develop. Remove from heat. Set aside.