Soak chia seeds in ½ cup of water for 30 minutes.
Add mint leaves, lime juice, sugar, and ½ cup water to a blender and blend to make a smooth mixture.
Transfer the mixture to a pitcher. Add the remaining 3 cups of chilled water to the pitcher and stir well.
Pass the mixture through a fine-mesh strainer.
Stir in soaked chia seeds.
Add a few ice cubes, lime round, and mint leaves to serving glasses. Pour the mint mixture over ice and serve chilled.