Boil potatoes until soft but firm. Cool them in an ice bath.
Once cooled, cut the potatoes into bite-size pieces. Add parsley, onion, cucumber, vinegar and oil; mix well.
Stir in chicken broth. If more broth is needed to moisten, add up to another ½ cup. Add 1 teaspoon sugar, and salt and pepper. Taste and add additional sugar, if desired.