Combine chicken, diced tomatoes with green chile peppers, chopped green chile peppers, sesame oil, sugar, chipotle chile peppers, garlic, and salt in a bowl. Cover bowl with plastic wrap and marinate chicken in the refrigerator, 1 hour to overnight. Drain chicken in a colander.
Heat olive oil in a large skillet over medium heat. Cook 1 tortilla in the hot oil for 5 seconds; flip tortilla and cook for 5 seconds more. Repeat with remaining tortillas.
Spoon about 1/2 cup chicken mixture onto each tortilla. Sprinkle Monterey Jack cheese over filling. Spoon filling in a line down the middle of a tortilla. Fold opposing edges of the tortilla to overlap the filling. Roll 1 of the opposing edges around the filling.
Place each chimichanga, seam-side down, in the hot oil of the same skillet until browned, about 3 minutes per side.