Prepare a grill or grill pan at medium-high heat.
Drizzle the ears of corn with 1 tablespoon of the olive oil, and season them all over with the salt and pepper. Get in there with your hands or a pastry brush to really get the seasonings and oil onto all of the kernels.
Grill the corn for about 15 minutes, rotating it every few minutes to ensure that all sides get a good char. Remove it from the grill and let it cool.
Coat the chicken thighs evenly with the BBQ sauce. Grill them for about 5 minutes per side, until they are cooked through and nicely charred. Set them aside to cool.
Slice the corn off of the cobs, then toss it with the avocado, nectarine, green onions, cilantro, lime juice, and the remaining tablespoon of olive oil. Taste for seasoning, adding more salt and pepper as needed.
Set out the romaine leaves on a serving platter. Dice the chicken, then spoon it onto the lettuce leaves. Top each leaf with a generous spoonful of the corn salad, and serve right away.