Rinse and cut the whole grapefruit into thin slice. Transfer into a jar with the thyme leaves
In a saucepan, add in 1 cup of water and the 2 cups of sugar. Bring the sugar solution to gentle simmer into the sugar crystals have melted. You now have syrup. Allow the syrup to cool to room temperature.
Pour the syrup over the grapefruit and thyme. Cover the grapefruit mixture with a tight lid. Place in a fridge for at least 12 hours. Preferably about 48 hours. This allows the grapefruit and thyme to infuse properly into the syrup.