Season the chicken breasts on both sides with the taco seasoning and a pinch of salt and pepper.
Heat the olive oil in a skillet over medium heat. Add the chicken and cook for about 6–7 minutes per side, until the internal temperature reaches 165°F (75°C). Remove from heat and let rest for a few minutes.
Shred the cooled chicken with two forks until it’s tender and pull-apart. If you like it juicier, you can shred while still warm.
Meanwhile, in a large bowl, combine the shredded cabbage, shredded carrot, and chopped cilantro.
Whisk together the lime juice, mayonnaise (or yogurt), lime zest if using, and a pinch of salt to make the slaw dressing. Pour over the cabbage mixture and toss to coat. Taste and adjust with more lime juice or salt as needed.
Assemble the tacos: warm the tortillas in a dry skillet or microwave until pliable. Pile on a generous portion of shredded chicken, then top with the cilantro lime slaw. Serve immediately.
If you like extra heat, add a few dashes of hot sauce or a slice of jalapeño.