Boil pomegranate juice in a medium saucepan until reduced to 3/4 cup, 15 to 20 minutes. Let cool. Whisk in vinegar, oil, salt, thyme, and pepper.
Mix salad greens, chives, parsley, walnuts, and pomegranate seeds gently with dressing in a very large salad bowl (or 2 bowls).
Make ahead: Dressing, up to 1 day, chilled.
Note: Nutritional analysis is per serving.