Stir together the sugar, fish sauce, lime juice, vinegar, water, chile and garlic until the sugar dissolves. Let stand for about 5 minutes.
In a small saucepan, heat the oil until shimmering. Add the shallots and cook over med.-high to high heat, stirring, until golden (don't let them burn!) - about 4 minutes or so. Drain on paper towels and sprinkle with salt. Let cool.
In a big bowl, toss the cabbage, carrots, onion, cilantro, mint and chicken.
Add the olive oil and dressing (the sugar, fish sauce, etc -- combination) and toss.
Sprinkle with the peanuts and shallots. Serve with the lime wedges.