Roast 2 boneless, skinless chicken breasts (generously brushed with olive oil) in a 350-degree oven on a cookies sheet for 30 minutes or until cooked through.
Cool for 10 to 15 minutes, chop into mince and place 1 cup of chicken in a medium mixing bowl. Gently mix the BBQ sauce with the chicken.
On 2 tortillas, evenly sprinkle 1/3 jack cheese on each, then 1/2 cup of the chicken chunks and 1/3 cheddar cheese on each.
Place the remaining tortillas on top of each and push down lightly. Place the quesadilla on a preheated griddle or two large skillets on medium heat.
Cook one side until lightly browned and gently turn, lightly brown the other side. Place on cutting board and use a pizza cutter to slice into pieces. Serve with your favourite salsa, sour cream or guacamole.