In a large skillet over medium heat, combine the oil and onion. Cook, stirring occasionally, until the onion softens, about 10 minutes.
Add the carrots, chayotes, allspice, garlic, and ginger. Cook for 5 minutes, or until the allspice is fragrant.
Add the chiles and vinegar. Cook, stirring occasionally, until the chiles soften, about 10 minutes.
Transfer the cooked mixture to a blender or food processor. Blend until smooth, leaving a vent open to allow steam to escape.
Using a fine-mesh strainer, strain the mixture, reserving the liquid and discarding the solids. Let it cool to room temperature.
Keep stored in the refrigerator for up to one month.