Heat oil in a large nonstick skillet over medium-high heat. Sprinkle the chicken evenly with salt, nutmeg, and pepper. Add chicken to pan; sauté 7 minutes or until golden. Remove the chicken from pan; keep warm.
Melt butter in pan over medium heat. Add onion; cook 4 minutes or until tender, stirring frequently. Add apple; cook 6 minutes or until golden, stirring frequently. Add garlic; cook 30 seconds, stirring constantly. Return chicken to pan; cook 2 minutes or until thoroughly heated, stirring frequently.
Heat tortillas according to package directions. Arrange 1/2 cup chicken mixture evenly over each tortilla.