For the prettiest chips, use blemish-free pears that are not quite ripe. A mandoline will help make the pear slices perfectly even.
Preheat oven to 200 degrees. Line a large baking sheet with parchment paper or a nonstick baking mat (such as a Silpat); set aside.
In a medium saucepan over medium-high heat, combine sugar with 1 cup water. Bring to a boil; cook, stirring occasionally, until sugar has dissolved, about 8 minutes. Reduce heat to medium-low; keep at a simmer as you proceed.
Using a mandoline or a very sharp knife, slice pear lengthwise as thinly as possible; make sure that each slice remains intact and is uniformly thick. Do not worry about removing seeds or the core (they soften during baking). Squeeze lemon halves over pear slices, coating both sides with juice. Place slices in simmering syrup; cook 2 minutes. Remove slices with a slotted spoon and place on the prepared baking sheet about 1 inch apart.
Bake pear slices until they are dry to the touch, about 2 hours. Using a small offset spatula, loosen edges of slices; use your hands to peel pears from the sheet, then flip them over. Return pears to oven; bake, checking frequently, until chips are completely dry and crisp (but not browned), about 20 minutes.
Chips can be kept in an airtight container at room temperature, layered with parchment paper, up to 2 days.