Bring a large pot of salted boil to a boil. Meanwhile, peel the cayote, then quarter them and remove the center sore with the seeds. Cut the chayote into ¼-inch slices. Add them to the boiling water and boil for 5 minutes, then drain.
While the chayote is boiling, heat the olive oil in a large skillet over medium heat. Add the onions and cook, stirring, for about 5 minutes until the start to soften. Add the garlic and cook, stirring, for another minute until the garlic blends in and turns golden. Add the drained chayote, tomatoes, and ½ cup water. Bring to a simmer, then cover the pot and continue to cook over low heat for about 10 minutes until the chayote is just barely tender. Taste and add salt and pepper to taste. Serve immediately.
Notes
Chayote will last for up to a month when it is stored in an air-tight container in the fridge to prevent drying out. A plastic bag or sealable container will work great.