What could cause muscle spasms in my chest?

Overuse. First, always make sure with your doctor that your chest pain is not cardiac or pulmonary. After that, look at the usage of your arms. Activities such as pushups, or frequent pushing/pulling/carrying of items can cause chest muscle discomfort. Other times, muscle spasms of the upper back can radiate to the chest muscles. Physical therapy/ massage or a muscle relaxant can help.