Using a vegetable peeler, cut the orange part of the peel from the stem end of the orange down to the navel end, forming long 3/4 to 1-inch-wide strips. Bring a heavy small saucepan of water to a boil. Add the peels and cook for 1 minute. Drain and then rinse the peels under cold water. Repeat cooking the peels in the saucepan with fresh boiling water and rinsing under cold water.
Stir the sugar and 1/2 cup of fresh water in a heavy small saucepan over medium-high heat until the sugar dissolves. Bring to a boil. Add the orange peels and simmer over medium-low heat until tender, about 15 minutes. Using tongs, transfer the peels to a sheet of parchment paper to dry slightly, about 1 hour.