Pack the onions tightly in a quart jar, pressing them down.
Combine vinegar, sugar, salt, and water in a saucepan and heat until the sugar and salt dissolve completely. Pour the hot brine over the onions until the onions are completely submerged. Tap the jar to remove air bubbles and add liquid if needed.
Cover tightly and allow the jar to cool to room temperature. Refrigerate for up to one month.