Preheat a large skillet over medium-high heat.
Cut the chicken into small cubes and put in a medium mixing bowl. Add the taco seasoning to the chicken and mix until all the chicken is coated.
Spread 1 Tablespoon of olive oil onto the skillet. Place the chicken in the skillet in an even layer. Sauté the chicken for 3-4 minutes per side until it's browned slightly.
Then top the chicken with salsa and toss the chicken to thoroughly coat the chicken with the salsa. Continue to cook the chicken until it's cooked through (internal temperature of 165 degrees Fahrenheit) for approximately 3-4 more minutes.
Remove the chicken from the skillet and set aside on a plate. Reduce the temperature to medium-low.
Lay a tortilla flat on a cutting board. Spread some cheese on half the tortilla, then put some of the chicken on top of the cheese, top off with more cheese. Fold the tortilla in half to make a half moon shape.
Once all the quesadillas are put together, put the remaining 1 Tablespoon of olive oil in the skillet and add 2 of the tortillas to the skillet at a time.
Cook until one side of the tortilla is golden brown (2-3 minutes). Flip and then cook until the other side is golden brown as well (2-3 minutes). Watch them closely as they brown quickly.
Remove the quesadillas onto a cutting board. Slice and serve immediately