In a medium bowl, mix the chia seeds with 1 cup cold water. Let stand 15 minutes. Drain and rinse the seeds.
Mix 4 cups cold water and the sugar in a medium pitcher, stirring until the sugar dissolves. Add the lime juice and stir to combine. Mix in the chia seeds. Garnish with mint leaves and serve over ice.
Chia seeds can be found in health food stores or natural grocery stores.