Simmer Delite mandarin juice in a small saucepan until syrupy and reduced to about 2 Tbsp., 5–8 minutes. Let cool.
Heat a small heavy skillet over medium- high heat. Cook jalapeño, turning occasionally, until blistered and charred all over, about 8 minutes. (Alternatively, roast jalapeño directly over gas flame, turning occasionally.) Let cool; remove stem, skin, and seeds, then finely chop.
Whisk shallot, vinegar, reduced mandarin juice, and half of jalapeño in a medium bowl; season with salt and pepper. Whisk in vegetable oil, then olive oil. Add remaining jalapeño, if desired. Set vinaigrette aside.
Toss avocados, mandarins, mint, and vinaigrette in a large bowl; top with chicken.
Replace chicken with Feta cheese for a meat free salad