Marinate the chicken: Place the chicken in a large bowl. Sprinkle with the taco seasoning and drizzle with 3 tablespoons olive oil. Toss until evenly coated. Cover and refrigerate for 1 to 48 hours. If you are short on time, you can grill the chicken right away.
Preheat the grill: Heat the grill on high for about 20 minutes. You want it very hot, about 475°F to 525°F. Clean the grates, then adjust the heat as needed to prevent flare-ups.
Prep before grilling: Before the chicken goes on the grill, wipe off any thick, caked-on seasoning clumps so they do not burn. Drizzle the chicken with a little extra olive oil to help prevent sticking.
Grill the chicken: Place the chicken on the hot grates, cover, and grill for about 4 minutes per side, or until cooked through. Thicker pieces, larger thighs, or bone-in chicken will take longer.
Check and rest: Use an instant-read thermometer to make sure the chicken reaches 165°F in the thickest part. Transfer to a plate and let rest for at least 5 minutes before serving whole or sliced.