Make a simple syrup by bringing the sugar and water to a boil in a small saucepan; allow to boil 1 minute; remove from heat.
Combine the syrup, lime juice, and basil in a blender; puree.
Pour the mixture into a container and cover; store in freezer until completely frozen, about 2 hours.
Break the frozen mixture into pieces and place in the blender; blend until smooth. Return to the container and cover. Store in freezer until ready to serve.
