Combine all of the sauce ingredients in a bowl, mix well, and set aside.
Preheat a gas grill on medium heat or a charcoal grill until the coals are ash white.
Grill the chicken until the internal temperature reaches 165 degrees, about 6-7 minutes. Remove from the grill and let cool. When cool, shred with 2 forks.
Arrange half of chips in a grill-safe pan or on a 15-by-10-by-1-inch disposable aluminum pan. Top with half of cheese. Repeat the layers. Top with the shredded chicken and pico de gallo.
Place the pan onto the grill and close the lid. Grill until the cheese is melted and bubbly, for 10-15 minutes. Top the nachos with avocado, drizzle with sauce, and serve immediately.