How to Make It
In a large nonreactive baking dish, mix 1/4 cup plus 2 tablespoons of the canola oil with 3 tablespoons of the lime juice, the garlic, jalape—o and 1 teaspoon of salt. Add the chicken, turn to coat and let stand at room temperature for 1 hour or refrigerate for up to 4 hours.
Roast the red and green peppers under the broiler or directly over a gas flame, turning occasionally, until charred all over, about 10 minutes. Transfer to a bowl, cover with plastic wrap and let steam for 10 minutes. Peel the peppers, discard the stems and seeds, then dice.
Meanwhile, in a medium skillet, heat 1/4 cup of the oil until shimmering. Add the tortilla strips and fry over high heat, turning frequently, until golden, about 2 minutes. Drain on paper towels and sprinkle with salt.
In a blender, combine the remaining 3/4 cup of oil with the cilantro, sugar, vinegar and the remaining 1/4 cup of lime juice and puree until smooth. Season the vinaigrette with salt and pepper.
Heat a large cast-iron grill pan and lightly rub it with oil. Remove the chicken from the marinade and scrape off any garlic and jalapeño bits. Grill the chicken over moderate heat, turning occasionally, until browned and cooked through, 10 to 12 minutes. Transfer to a work surface and let stand for 10 minutes, then cut into 3/4-inch dice.
In a large bowl, combine the roasted peppers with the tomatoes, avocados, onion, jicama, tomatillos and chicken. Add the vinaigrette and toss gently to coat; season with salt and pepper. Transfer the salad to a large platter, scatter the fried tortilla strips on top and serve.