Is running bad if i have chronic back injury/pain?

Depends!: There is not a right or wrong answer. Many people feel better if they get regular aerobic exercise (heart rate pushed up above 100 beats per minute), at least 30 minutes three times a week. If running aggravates your back (or knees or ankles, etc), try another aerobic exercise: swimming, water aerobics, cycling (outside or on a stationary bicycle), and other exercises. Find something practical.

No unless it : Aggravates your symptoms then you may want to cross train and work on core strength prior to trying to return to running. Exercise, in general, is usually beneficial for back health.