Mix olive oil, lemon juice, garlic powder, smoked paprika, oregano, salt, and pepper in a small bowl. Pat the chicken thighs completely dry—moisture is the enemy of crispiness, and this step is what most home cooks skip even though it takes literally 60 seconds.
Coat all eight thighs with the marinade, making sure the spice mix gets under the skin. Let them sit at room temperature for 15-20 minutes while you prep the grill because this marinade needs contact time to actually season the meat, not just sit on top of it.
Heat your grill to medium-high heat and oil the grates with a clean cloth. I learned this the hard way: ungreased grates mean skin sticks, tears, and frustration—oiled grates mean burnished skin that looks restaurant-ready.
Place thighs skin-side down on the grill and resist the urge to touch them for 8-10 minutes. The skin needs uninterrupted heat to render the fat and turn golden-brown, and every flip restarts that process which defeats the entire purpose of this 4th of july grilled chicken family recipe technique.
Flip the thighs and cook for another 15-18 minutes until internal temperature reaches 165°F at the thickest part. I check with an instant-read thermometer because visual doneness is guesswork, and guesswork is how undercooked chicken happens at parties.
Move the corn to the grill grates (or wrap in foil if you're worried about losing it) and turn every 2-3 minutes until the kernels show char in spots. The charred bits on corn taste like actual summer, which is the whole reason to grill it instead of boiling it in a pot.
While chicken and corn finish, whisk together mayonnaise, apple cider vinegar, sugar, and a pinch of salt in a large bowl. Toss shredded carrots, red cabbage, and fresh parsley into the dressing and let it sit for 5 minutes so the vegetables soften just slightly and the flavors marry.