Warm the vegetable oil in a small skillet over medium-high heat. Add the chiles and cook, turning, until the skins blister, about 5 minutes. Let cool, then stem and finely chop.
Combine the chopped chiles with the mango, cilantro, lime juice and onion in a bowl. Season with salt and pepper.
Mash the avocados in a medium bowl. Mix in the mango-chile mixture and the jicama. Season with salt and pepper and serve with chips.