Slice star fruit crosswise with slicer into 1/16-inch-thick slices.
Bring sugar and water to a boil in a 2-quart heavy saucepan, stirring until sugar is dissolved. Add star fruit, then remove from heat and let stand, uncovered, 15 minutes. Pour star fruit into a sieve set over a bowl and drain 15 minutes. Reserve syrup for quince apple strudels .
Put oven rack in middle position and preheat oven to 200°F. Put liner on a large (17- by 11-inch) baking sheet, then arrange star-fruit slices in 1 layer on liner (discard extra along with any broken slices). Bake until dry, 1 to 1 1/4 hours. Immediately transfer chips to a rack to cool.