Combine the thyme, sugar and water in a saucepan over a low heat until the sugar is dissolved. Let simmer for 20 to 30 minutes or until the syrup smells like thyme. Remove from the heat and let cool completely. Strain the syrup and transfer to a bottle. Makes about a cup and a half of syrup. Refrigerate for up to 2 weeks.
To Make the Drink:
Combine all ingredients in a shaker. Shake. Pour into chilled glass.