In a large serving bowl, toss chicken with 1 Tbsp. oil, 2 Tbsp. lime juice, chili powder and salt.
Add remaining ingredients and remaining 1 Tbsp. each oil and lime juice; gently toss to combine until well coated. Serve immediately.
I had to add some additional spices to compensate for the use of Chili powder. Mexican cooking has far more depth than was is offered here.