Whisk together marinade ingredients in a small bowl. Remove 3 Tbsp. of the marinade for later use, and add the remaining marinade to a large ziplock bag. Add the chicken, and toss to coat.
Then refrigerate the mixture for at least 1 hour (up to 8 hours). When ready to cook, remove the chicken from the marinade, and season generously on both sides with salt and pepper.
Heat 2 tablespoons of oil in a large sauce pan over medium-high heat. Add the (drained and seasoned) chicken breasts and let cook without touching for 5 minutes. Flip the chicken breasts over, and cook for an additional 3-5 minutes until no longer pink inside and juices run clear. Remove chicken and set aside on a plate to cool.
Add the remaining 2 tablespoons. oil to the pan and heat over medium-high heat. Add peppers, mushrooms and onions, and cook for about 7-10 minutes until crisp-tender, stirring frequently.
During the last few minutes that the vegetables are cooking, cut the chicken breasts into thin strips against the grain. When the vegetables are ready, add the chicken strips to the vegetable mixture. Reduce heat to medium-low, and drizzle with the reserved marinade and stir to coat. (Watch closely so that the tequila in the marinade does not flame up.) Cook for 2 minutes, then season with additional salt and pepper if needed.