kesten

1. (the nut) chestnut
   Zimi na ulici kupujemo pečene kestene. — In winter we buy roasted chestnuts on the street.
   Deca skupljaju kestenje u parku. — The kids are collecting chestnuts in the park.
2. (the tree) chestnut tree
   Ulica je bila puna starih kestenova. — The street was lined with old chestnut trees.

For the nuts, the collective plural kestenje is often used.