Combine the sugar, salt, vinegar and water in a pan over medium heat. Heat the mixture until the salt and sugar completely dissolve. Set this aside to cool for a few minutes.
Shred your carrot and cut the onions or chives into small pieces. Add these to the bean sprouts in a medium sized bowl.
Pour the brine over the vegetables. The liquid will not completely cover the vegetables. Stir a bit, then leave the bowl for about an hour. The brne will pull the liquid from the vegetables and eventually the liquid will cover them completely. I like to toss the mixture a few times during this hour.
You can serve you pickled bean sprouts right away but I prefer to put them in a mason jar and let them sit in the fridge for a day (or up to a week) before serving!