Using a medium sized saucepan, add chicken and saute over medium- high heat approx 20 minutes.
Add in sugar, lime juice, red wine vinegar, garlic, green onions, cilantro, salt, and pepper. Reduce heat and simmer for 10 minutes.
Using an iron skillet, heat over medium heat.
One at a time, put a tortilla in the preheated skillet. Warm one side, then flip to warm the 2nd side. Continue with the rest of the tortillas.
Using 1/10th of the chicken mix, fill each warm tortilla. Add lettuce, tomato, salsa, and Monterey Jack cheese. Serve