In a stockpot, place potatoes and chayotes with enough water to cover them. Boil for 15 minutes or until fork tender, add salt at the last 3 minutes of boiling. Remove from heat, remove from water and let cool. Remove soft pit from chayote halves with a melon baller and cut both potatoes and chayotes in ½” cubes.
In a stockpot, boil 5 cups water. Add tomatillos, garlic cloves, jalapeño and onion. Continue boiling for 12 minutes or until tomatillos are tender and dark in color.
In a blender, add tomatillos, garlic cloves, jalapeño, onion, cilantro, chicken bouillon and 1 ½ cups of the water they were boiled in. Blend until smooth.
In a large saucepan, heat oil over medium heat, carefully pour in tomatillo sauce, add potato and chayote cubes. Cook for 10 minutes covered, stirring frequently.
Transfer to a serving dish, garnish with a cilantro sprig and serve.