Whisk the lime juice, vegetable oil, jalapeno and 1/2 teaspoon salt in a medium bowl.
Peel and slice the chayotes into thin wedges. Peel the jicama; thinly slice lengthwise, then thinly slice crosswise into strips. Thinly slice the carrots.
Toss the vegetables with the dressing and season with salt. Cover and refrigerate up to 4 hours.