You should cite each chapter, but you can do it a couple different ways. If you're citing only a few contributions from an edited volume, you may want to cite each one in full, like so:
Smith, John. Date. "Title." In Book Title, edited by Jane Doe, pages. Place: Publisher.
But if you have several, you can cross-reference.
Smith, John. Date. "Title." In Doe, pages.
Jones, Sue. Date. "Title." In Doe, pages.
Doe, Jane. Date. Book Title. Place: Publisher.
Does that make sense?