Heat a large skillet over low heat with the oil. Add the onions and cook low-and-slow for about 15-20 minutes, until the onions begin to turn a deep, golden brown. Add the garlic, a big pinch of salt and pepper, and the ground thyme. Turn the heat up to high and add the cider. Cook for about 5 minutes more, until the cider mixture reduces by half. Remove from heat and let cool.
Once the onions have cooled, place them into a mixing bowl with the Greek yogurt. Taste and season more, if needed. Put into a serving bowl and chill until ready to eat. Top with chives before serving.