Core and chop the plums and add them to a non-reactive mixing bowl. Add the sugar and stir until the plums are thoroughly coated.
Cover the bowl with plastic wrap and place in the fridge. Let the mixture sit for at least 24 hours. While the mixture is resting, the sugar will begin to extract the juice from the plums, creating a rich plum syrup.
Remove the mixture from the fridge and strain the syrup and any excess sugar into a new mixing bowl. Firmly press on the plums to release any remaining juice. Whisk in the vinegar, dissolving the sugar as you go. Transfer the shrub into a bottle for storage.
The flavors will continue to develop as time passes. The vinegar will mellow and new notes of fruit will emerge.