Char chili and bell peppers over gas flame or in broiler until blackened on all sides. Enclose in plastic bag 10 minutes. Peel, seed and cut chili and peppers into matchstick-size strips. Heat 1 tablespoon oil in heavy large skillet over medium-high heat. Add chayote and saute; just until crisp-tender, about 1 minute. Cool completely. Combine Sherry wine vinegar and 2 teaspoons Latin Spice Mix in medium bowl. Gradually whisk in 1/2 cup olive oil. Mix in fresh cilantro. Season vinaigrette to taste with salt and pepper. Combine chayote, chili and peppers in bowl. Toss with enough vinaigrette to coat. Season with salt and pepper. (Can be made 1 day ahead. Cover; refrigerate.) *A fresh green chili, often called a pasilla, available at Latin American markets and some supermarkets. **A squash-like, pear-shaped fruit similar in flavor to cucumber and often prepared like squash; available at Latin American markets and some supermarkets.