In a saucepan, add in the chopped kiwi, sugar, and water. Stir until combined. Place over medium heat and let cook until sugar is dissolved (about 10 minutes).
Remove and place in a blender. Puree until completely smooth.
Place the puree in a container and let chill in the fridge until completely cooled. I left mine in for 5 hours until chilled. Overnight would work too.
Place in the ice cream maker for the recommended time for your ice cream maker. Mine recommends no longer than 20 minutes.
Place in a freezer safe container and freeze for 2 hours or until very firm. Scoop and serve!