Mix all ingredients except eggs in medium saucepan. Bring to boil, then reduce heat to low and simmer for 5 minutes.

Place peeled eggs in a glass jar (I use a quart mason jar), and carefully pour contents of saucepan over the eggs. Let cool, put on lid, and store in refrigerator for 24 hours, turning occasionally to pickle the eggs evenly.

To serve, remove beets and eggs with slotted spoon, and cut eggs in quarters.