Preheat your grill over medium high heat. We have a Traeger grill, and I set it to 375ºF. Clean the grill grates.
Rub both sides of the chicken with olive oil. Season both sides of the chicken generously with the blackened seasoning.
Grill breast skin side UP until the chicken has an internal temperature of 165ºF, about 45 minutes on my Traeger grill. I never flip the chicken, just grill it skin side up the whole time.
While the chicken is grilling, make the lime aioli. In a small bowl, combine the mayo, lime zest, lime juice, salt + pepper. Stir to combine. Taste and adjust the seasoning if desired.
Remove from the grill and allow to rest for 5 minutes. Then carve the chicken and serve with the lime aioli. I love this meal with my roasted radishes and my sauteed shaved brussels sprouts.
Leftovers will keep in an airtight container refrigerated for at least 5 days.