Place the watermelon chunks in the bowl of a blender or a food processor, replace the top, and blend on high speed until very smooth. Turn the blender off.
Transfer the watermelon puree to a mixing bowl and add the sugar and lime juice.
Stir with a wooden spoon until the sugar is completely dissolved, about 2 to 3 minutes.
Transfer the mixing bowl to the freezer and freeze for 30 minutes.
Remove the bowl from the freezer and use a fork to scrape any ice crystals from the sides of the bowl. Stir to incorporate the crystals. Return to the freezer.
Repeat this scraping procedure every 30 minutes, or until the consistency is "snowy" when scraped with a fork or spoon, at least 4 hours. Then scoop into bowls or dessert glasses and serve.
YIELD: 6 to 8 servings