For chive butter: 2 sticks unsalted butter, softened 2 cups coarsely chopped chives 1/2 teaspoon salt 1 teaspoon dijon mustard 1/2 teaspoon lemon juice Salt and pepper to taste
For chive butter: Place chives and 1/2 teaspoon salt into a food processor and process until smooth. Place butter in a medium bowl and stir until smooth. Add chive mixture, dijon and lemon juice to the butter and mix well. Season to taste with salt and pepper mixing well. Transfer chive butter to a sheet of parchment paper in dolops horizontally in a line across the middle of the parchment. Fold the bottom half of the parchment in half over the butter and with a ruler, press it towards you to make a log. Twist the ends of the parchment (like a tootsie roll) and freeze for up to 6 months. Chive butter can be made ahead and frozen for many uses. Peel back husks, being careful not to completely remove them and remove silk. Fold husks back around corn cobb.
Place corn in a tub or sink of cold water. Let soak for 15 minutes.
In a small bowl, combine basil and butter. Set aside.
Remove corn from water and pull back husks. Dry corn with a paper towel. Spread chive butter over corn. Fold husks back over corn. Repeat with remaining corn cobbs.
Grill corn for about 12-15 minutes, turning frequently.
Remove corn from grill and pull off husks. Season corn with salt and serve.