Add 1 1/2 tablespoons olive oil to dutch oven or 12" skillet and heat over MED HIGH heat. Add chicken, sprinkle with half of the fajita seasoning and cook about 2 minutes. Turn chicken pieces over (or give it a good stir) and cook the other side for another 1-2 minutes. Remove chicken to a plate and set aside.
Add remaining 1 1/2 tablespoons olive oil to dutch oven and add in onions and peppers and remaining fajita seasoning. Cook, stirring occasionally, about 4-5 minutes, until softened and slightly charred. Add garlic, stir, and cook about 30 seconds, then remove vegetable mixture to the plate with the chicken and set aside.
Pour in chicken stock, heavy cream, diced tomatoes and chiles, pasta, and a pinch of salt and black pepper. Use a wooden spoon to carefully loosen the browned bits from the bottom of the skillet and bring to a boil. Once boiling, reduce heat to a low boil (usually about a MED LOW heat should work), cover, and cook about 15 minutes, stirring occasionally.
After 15 minutes, most of the cooking liquid should be absorbed. If it's not, cook another 3-5 minutes. Return the chicken and vegetables to the pot and stir to heat through.
Serve garnished with diced green onions and minced fresh parsley or cilantro and with a squeeze of a lime wedge.