In a large glass jar or pitcher, combine the rum and orange peels. Cover and refrigerate for about five days. Strain and remove the orange peels.

Combine the sugar and water in a small saucepan and simmer until the sugar has dissolved and the water has reduced by half. Let chill to room temperature before combining with the strained rum. Chill in the refrigerator for at least an hour. Serve in glasses with ice, garnished with the orange slices.