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Place the mango chunks in the food processor and puree until smooth. You should have about 3 cups of puree. Place the 3 cups of puree in a mixing bowl and stir in the simple syrup, lime juice, and chili powder. Pour the mixture into a shallow dish and place in the freezer. Freeze for at least 3 hours and up to overnight.
If using an ice cream maker, pour into maker and freeze according to manufacturers directions. Transfer the sorbet to a freezable container and freeze until firm, about 1 to 2 hours.
Serve cold, sprinkled with a little coarse salt and more chili powder, if desired.