Season the chicken on both sides with salt and pepper. Drizzle with a small amount of oil.
Heat a grill pan or grill over medium heat. Grill the chicken on both sides and cook to an internal temperature of 160 degrees using a thermometer. Remove from the pan and set aside. Slice before serving.Grill the taco shells on both sides to warm.
For the mole sauce: whisk together all of the ingredients for the sauce. Simmer, stirring occasionally until the sauce becomes thick and rich.
Top the taco shells with lettuce, chicken, tomatoes, and avocado. Drizzle with sauce (save any extra to serve on the side if desired). Garnish with cilantro, lime wedge, and jalapeno.