The structure in the cell nucleus that houses the cell's genetic information is the chromatin.

Here's why:

* Chromatin: Chromatin is a complex of DNA and proteins that make up chromosomes. It is essentially the "packaging" for DNA within the nucleus.

* DNA: Deoxyribonucleic acid (DNA) is the molecule that carries the genetic instructions for an organism.

* Chromosomes: Chromosomes are long, thread-like structures made of DNA and proteins. They are condensed forms of chromatin, which become visible during cell division.

So, while the nucleus itself contains the genetic information, it's the chromatin within the nucleus that physically houses and organizes the DNA.