The phage DNA that integrates into a host chromosome is called a prophage.

Here's a breakdown:

* Phage: A virus that infects bacteria.

* Integration: The process where the phage DNA becomes part of the host's bacterial chromosome.

* Prophage: The integrated phage DNA within the host chromosome.

The prophage can remain dormant within the host's genome for generations. However, under certain conditions, it can reactivate, leading to the production of new phages. This process is called lysogeny.