The Complete Guide to Interpreting Your Dreams

by Stearn Robinson - Tom Corbett
The meaning varies greatly with the action.

If you were splitting or opening the chestnuts, you will solve a mystery or a problem which has been plaguing you.

If you cooked the nuts, you are in danger of being exploited by someone you trust; eating chestnuts in a dream predicts happy relations (sexual and/or social as may apply) with the opposite sex.

Lucky you.

Ten Thousand Dream Interpretation

by Gustavus Hindman Miller
To dream of handling chestnuts, foretells losses in a business way, but indicates an agreeable companion through life. Eating them, denotes sorrow for a time, but final happiness.

For a young woman to dream of eating or trying her fortune with them, she will have a well-to-do lover and comparative plenty.

The Complete Dream Book

by Gillian Holloway
Eating chestnuts, raw, boiled or roasted, is a dream of good fortune in love affairs.

An unmarried woman who has this dream will make a good marriage with a man who will be faithful and reasonably successful in business. Men who have this dream will have devoted wives.