First, make the rhubarb syrup. Chop the rhubarb stalks into 1/2 inch pieces. Put in a medium-size saucepan along with the sugar and water. Heat to boiling, then simmer until rhubarb is soft and falling apart.
Using a fine-mesh sieve, strain the rhubarb into a large jar. Press on the solid rhubarb to extract all the liquid. You can save the rhubarb solids...I eat them plain!
Mix in the lime juice. Add 8-12 ice cubes to cool the mixture. Stir until the cubes are melted, then add the vodka. Slice off a thin strip of rhubarb if you have extra stalks, and twist it to add a fun flourish to each person's drink glass!