For the beer-braised chicken: Preheat the oven to 350 degrees F. Heat a large skillet over high heat. Season the chicken with 1 tablespoon salt and 2 teaspoons pepper.
Add the grapeseed oil to the skillet and sear the chicken thighs on all sides until golden brown, 2 to 3 minutes per side. Do not overcrowd the pan or the chicken will steam instead of sear; work in batches if necessary. Transfer the chicken to an oven-safe casserole dish with the onion, carrots and celery.
Add the beer to the drippings in the skillet and cook, scraping up the bits on the bottom of the pan with a wooden spoon, until the liquid is reduced by half. Add the chicken stock and brown sugar and bring to a simmer. Season the braising liquid with salt and pepper. Pour the braising liquid over the chicken and cover the pan with foil.
Transfer the casserole dish to the oven and cook until the chicken is tender, 45 to 60 minutes. Remove the pan from the oven, remove the foil and allow the chicken to cool in the braising liquid. Shred the chicken meat.
For the vinaigrette: In a blender, combine the lime juice, chili sauce, vinegar, mustard, garlic and oregano and puree. Slowly add the olive and vegetable oils while the blender is running. Season the vinaigrette with salt and pepper.
For the salad: Arrange a layer of the lettuce leaves on each plate. Spread 1/4 cup each of the tomatoes, olives, Cheddar and chicken over the lettuce. Drizzle with some vinaigrette and then repeat with an additional layer of lettuce, tomatoes, olives, Cheddar and chicken. Add a final drizzle of vinaigrette and serve with the guacamole, sour cream and tortilla chips on the side.