Cut chicken breasts into ½” strips. Mix lime juice, olive oil, garlic, salt, cumin, chili powder, jalapeno and cilantro together in a zip-top bag or shallow dish. Add the chicken, mix well, cover and let marinate at room temperature for 30 minutes or up to 8 hours in the refrigerator.
Remove the chicken from the marinade. Heat 1 Tbsp oil in a large skillet. Add chicken in a single layer, working in batches if needed. Cook chicken on med-high heat for 2-3 minutes, until they are seared and cooked through. Turn over and sear on the 2nd side. Remove to a cutting board and cover with aluminum foil. If there is more chicken to be browned, add 1 Tbsp to skillet, if needed, heat, then add chicken. Sear on both sides until cooked through, remove to a cutting board and cover with aluminum foil.
Add 1 Tbsp oil to the skillet and heat. As soon as the oil is hot, add the onion, peppers and asparagus to the pan. Scrape up some of the browned bits from the chicken and stir to coat the vegetables with the oil and brown bits. Spread the vegetables in an even layer in the pan. Cook 2 minutes. Stir, then continue to cook for 2 minutes.
Serve chicken and veggies at once in warm tortillas with shredded cheese, salsa, avocado, sour cream and lettuce, as desired.