Combine shredded chicken and 1/2 cup of BBQ sauce in a small bowl. Reserve the remaining 1/3 cup of BBQ sauce for later. You can use any kind of leftover chicken for this recipe, we like using either rotisserie chicken for pulled chicken or grilled chicken thighs shredded.
Spread out tortilla chips on a rimmed cookie sheet. Top with half of the shredded colby jack and cheddar cheese. Layer the BBQ chicken, beans, olives, tomatoes, and the rest of the cheese on the chips. Put the remaining BBQ sauce in a plastic bag, snip the corner, and pipe it evenly across the top of the cheese.
Place the cookie sheet in the oven or on the grill for about 10 minutes or until the cheese is hot and melted. Remove from the oven or grill.
Scoop the sour cream into a small plastic bag, snip the corner, and pipe it evenly across the top of the nachos. Garnish with cilantro and lime slices. Serve immediately and enjoy your delicious BBQ chicken nachos!