Trim the base of each endive head and gently separate the leaves until you have about 24 intact, cup-shaped leaves. Rinse and pat thoroughly dry.
In a small bowl, stir the goat cheese, Greek yogurt, olive oil, honey, salt and pepper until smooth and spreadable, about 1 minute.
Spoon or pipe about 1 teaspoon of the goat cheese mixture into each endive leaf.
Top each boat with pomegranate arils, chopped walnuts and chives.
Arrange on a platter and serve within 2 hours; if making ahead, refrigerate up to 4 hours and add the walnuts just before serving so they stay crisp.