Butternut squash tastes like a whole new vegetable when grilled—crisp, bright and not overly sweet. Slideshow: Butternut Squash Recipes
Stir together the shallots, vinegar, salt, sugar and pepper in a small bowl. Slowly whisk in the olive oil until well combined. Set aside for at least 30 minutes for shallots to mellow.
Heat a charcoal or gas grill to moderate heat. Grill the sliced squash, flipping when grill marks appear and the squash has softened slightly, 7 to 8 minutes per side. Remove from the heat and arrange in a shallow serving dish. Cover tightly with aluminum foil to keep warm and let steam, covered, for 10 minutes.
Spoon the vinaigrette over the grilled squash, then garnish with the chopped chives. Serve warm.
The shallot vinaigrette can be made up to 12 hours ahead of time and stored at room temperature in an airtight container.