Acupuncture is indeed an effective and safe way to help relieve chronic back pain. 

How Acupuncture Works
The modern scientific explanation is needling the acupuncture points stimulates the nervous system to release chemicals in the muscles, spinal cord, and brain, including endorphins, encephalin and other neurochemicals. These natural chemicals may either change the pain experience or trigger the release of other chemicals and hormones that influence the body’s own internal regulating system.

This can bring about a normalizing effect on neuroendocrine (nerve and hormone) function. The improved energy and biochemical balance produced by acupuncture results in stimulating the body’s natural healing abilities, and in promoting physical and emotional well-being.

References 

Liu L, Skinner M, McDonough S, Mabire L, Baxter GD. Acupuncture for low back pain: an overview of systematic reviews. Evid Based Complement Alternat Med. 2015.

Furlan AD, Yazdi F, Tsertsvadze A, Gross A, Van Tulder M, Santaguida L, Cherkin D, Gagnier J, Ammendolia C, Ansari MT, Ostermann T, Dryden T, Doucette S, Skidmore B, Daniel R, Tsouros S, Weeks L, Galipeau J. Complementary and alternative therapies for back pain II. Evid Rep Technol Assess. 2010 Oct;(194):1-764.