Preheat a barbecue to a medium-high heat.
Cut both grapefruits into halves.
Use 1 tablespoon of olive oil to brush lightly on the cut sides of the grapefruits.
Take 1 tablespoon of honey and drizzle it over the grapefruits.
Place the cut side down on the grill, and cook for about 2 minutes.
Turn the grapefruit halves on their side and grill for another 2 minutes or so.
Remove from the grill and set on a plate to cool.
Squeeze the juice from one half of one grapefruit (only) into a bowl. Add the rest of the olive oil and honey, mustard, chives, salt, and pepper, and whisk thoroughly to combine.
Add the salad greens, chicken, feta, and nuts to a large bowl.
Separate the remaining grilled grapefruit halves and add them to the salad bowl.
Drizzle the dressing over the salad and serve immediately.