Preheat grill pan or outdoor grill to high. Coat chicken in extra-virgin olive oil, a generous drizzle. Combine the grill seasoning with cumin and thyme and sprinkle evenly over the chicken. Grill the meat 5 to 6 minutes on each side. Remove from heat and cool until easy to handle.
While chicken cooks, heat a skillet over medium-high heat. Add 1 tablespoon extra-virgin olive oil, a turn of the pan, the garlic and onion, cook together a few minutes then add the tomatillos. Cook together 3 to 4 minutes just to take the bitter edge off the tomatillo then remove from heat.
In a large bowl, combine the diced peppers, celery, olives and hominy. Dice and add the chicken. Add the hot sauce and the lime juice to the salad and dress with 2 tablespoons extra-virgin olive oil, eyeball it. Toss the salad then add in the tomatillo mixture and combine. Season the salad with salt and pepper, to taste, and serve with bits of tortilla chips as garnish.