In a small saucepan, combine the water and sugar. Heat over medium heat, stirring until the sugar is completely dissolved. Remove from heat and let cool.

In a blender, combine the chopped kiwis, lime juice, lime zest, and the cooled sugar syrup. Blend until smooth.

Pour the mixture into a mixing bowl and refrigerate for at least 2 hours or until well chilled.

Once chilled, pour the mixture into an ice cream maker and churn according to the manufacturer's instructions until it reaches a soft-serve consistency.

Transfer the sorbet to an airtight container and freeze for at least 2 hours to firm up before serving.