Heat a grill to medium, about 450 degrees. Alternately, you could heat a skillet over medium-high heat. Cut the lemon in half, and cut the white ends off the chives. Brush the chives lightly with olive oil and grill for just a minute or so or just until browned, turning often to keep them from burning. Add the lemons face down on the grill and cook just until browned, about 2 minutes.
Make the Dressing
Add all the ingredients except oil to your blender. Pulse until everything is broken down slightly.
Turn the blender on low-medium, and slowly drizzle the oil in as it blends until incorporated. Season to taste.
To store: Transfer to an airtight container and store in the refrigerator for 4-5 days.