In a medium bowl, combine olive oil, minced garlic, ground cumin, smoked paprika, chili powder, salt, black pepper, and juice of 1 lime to create the marinade.
Add the chicken breasts to the marinade and toss to coat evenly. Cover and refrigerate for at least 15 minutes.
Preheat a grill or grill pan over medium-high heat.
Remove the chicken from the marinade and grill for 5-6 minutes on each side, or until the internal temperature reaches 165°F (74°C) and the chicken is cooked through.
Transfer the grilled chicken to a cutting board and let it rest for 5 minutes before slicing into thin strips.
In a small bowl, mix sour cream, lime juice, and 1/4 teaspoon salt to make the lime crema. Set aside.
Warm the corn tortillas on the grill for about 30 seconds per side until pliable and slightly charred.
Assemble the tacos by placing sliced grilled chicken on each tortilla, then topping with shredded cabbage, diced red onion, chopped cilantro, and avocado slices.
Drizzle each taco with the lime crema before serving.