Stir together coconut milk, sugar, and lime juice in a small metal bowl, until sugar is dissolved, then quick-chill in a metal bowl set in a larger bowl of ice and cold water, stirring occasionally, about 6 minutes.
Cut melon in half and discard seeds. Scoop melon into balls.
Divide the melon equally among dishes, and pour coconut milk over the top. Serve immediately.
If desired you may substitute the honey dew melon with cantaloupe, or other sweet melon of your choice.
* I hav also used Canary Island Melon and Santa Claus Melon, and they both were good as well.*