Could you be addicted to depression?

Sort of: You would need to explore this in therapy to truly find out. But, often we are drawn to things that harm us or have harmed us in the past. This is referred to as a repetition compulsion, or a compulsion to repeat. It's a hint from your psychological mind that you need to work through something.

Depression: That perhaps would be labeled chronic depression.

I'm not sure what: You mean. When you ask if you are addicted to depression. Do you mean that it makes you feel good, 'high' to be depressed? I don't think anyone does. Usually depression comes and goes. If you are always feeling depressed, then i would agree with dr. Ali, that you have chronic depression, which seems not to lift at all. See a good therapist and work on what is bothering you. Consider medication too.