In a bowl, combine the olive oil, lime juice, lime zest, cumin, chili powder, garlic powder, salt, and pepper. Add the chicken breasts and coat them thoroughly. Cover and let marinate for at least 30 minutes (or up to 2 hours in the refrigerator for more flavor).
Preheat a grill or skillet over medium-high heat. Remove the chicken from the marinade and cook for about 6-7 minutes per side, or until the internal temperature reaches 165°F (75°C) and the chicken is golden brown. Remove from heat and let rest for 5 minutes.
While the chicken is resting, warm the corn tortillas on the grill or in a skillet until pliable.
Thinly slice the cooked chicken breast against the grain.
Place a few slices of chicken in each warm tortilla. Top with shredded red cabbage and sliced avocado.
Add fresh cilantro on top and serve with lime wedges on the side for an extra zesty kick.
Notes
For best flavor, marinate the chicken for up to 2 hours.