Roughly chop the basil flowers (or leaves) and stir with the sugar and water in a medium saucepan. Place over medium heat, bring to a boil and then reduce heat to low, simmering for 5 minutes.
Let the syrup stand, with the Thai basil left in, until completely cooled.
Strain the steeped syrup through a fine mesh sieve into a container with a spout for easy pouring later. This can be made up to 5 days in advance.
To serve, pour about 3 tablespoons of the syrup into a glass, stir in 1 tablespoon of lime juice and fill the glass with ice, topping off with about 8 ounces of carbonated water.