Cut the ends off of the zucchinis. Then cut them lengthwise into ¼ inch thick slices. You want to have approximately 16 slices. A mandoline is really helpful here.
Heat a skillet on medium high. Using just enough oil to prevent the zucchini slices from sticking, cook the them until they are softening and flexible but not all of the way cooked. It will take approximately 3 minutes per side.
In a mixing bowl, combine the chicken and green enchilada sauce. Stir until well mixed.
Spoon half of the red enchilada sauce into a glass 9x13 baking dish. Use the back of a spoon to evenly spread the sauce across the bottom of the dish.
When the zucchini is cool enough to handle, place a spoonful of chicken in the center of a zucchini slice. Fold one end of the zucchini over the chicken, then fold the other end over. Place it seam side down in the baking dish.
Repeat for the rest of the zucchini slices, evenly portioning out the chicken.
Dollop the remainder of the red enchilada sauce on top of each zucchini roll.
Sprinkle cheese over the top if adding it.
Cover the baking dish with foil.
Bake for 20 minutes.
If the zucchini slices aren’t long enough to make rollups, sandwich the chicken filling between two zucchini pieces instead.
You can substitute any plain shredded chicken for the canned chicken.