The Chromatic Scale includes all twelve notes (see theory lesson). There are many different ways to play a chromatic scale, but I will show one of my favorite fingerings in the link below.
When you are playing a chromatic scale, it sounds good when you start and end on notes in the key you are playing. The notes that are not in key you can use as "passing tones". This is a Jazz term for notes that you play in between notes that are in key.
Print Chromatic Scale Fingering (pdf)