"I am going straight to my parents' house."
Translation:Je vais directement chez mes parents.
Essentially, "chez" is the preposition you use when referring to a person, or a person's place. "Chez mes parents", "Chez le dentiste", etc. This link: http://french.about.com/od/grammar/a/preposition_chez.htm explains it in more detail, and shows more uses of it.
Read this @ you'll understand why :)