Can doing chin ups relieve back pain?

Probably not: First deternine the cause of your back pain. Chin ups are more likely to build your biceps and shoulder girdle muscles. Consider a trial of core strenghtening exercises as a better option in addition to postural changes and altered lifting habits.

Possibly: I do not recall seeing chin ups as a good exercise for back pain however, theoretically they may help because the strengthen the latissimus dorsi muscle which is a hugh muscle that contributes to the muscular "corset" that protects the spine.