Special equipment: Four 4-ounce ice-pop molds or six 3-ounce molds, 4 or 6 ice-pop sticks
Bring the sugar and 1/4 cup water to a simmer in a small saucepan. Cook over medium heat, stirring occasionally, until the sugar is completely melted, about 5 minutes. Turn off the heat, add the basil and stir until completely wilted. Let cool completely at room temperature, at least 30 minutes.
Meanwhile, finely mince the chile (seeded for less heat, if desired). Add the salt to the minced chile, and run your knife through the mixture several times until the salt starts to turn light pink; set aside.
Put the watermelon and lime juice in a blender. Strain the basil syrup into the blender, pressing the basil in the strainer with the back of a spoon to extract as much flavor as possible; discard the basil. Puree the watermelon mixture until completely smooth, scraping down the sides of the blender partway through if needed. Transfer the mixture to a large liquid measuring cup with a pouring spout.
Pour the mixture into the ice-pop molds, leaving 1/4 inch of space at the top (the mixture will expand). Insert the sticks. Freeze until solid, 5 hours to overnight. Unmold, and sprinkle 1 or both sides of the pops with the chili salt, depending on how spicy you want your pops. Serve immediately with any remaining chili salt on the side.
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