The chills you get when listening to music are caused by the release of dopamine in your body.
Scientists recruited people who reliably get shivers when listening to an affective score. The chills are a consistent, in the moment measure of pleasure than asking how test subjects felt. Scientists used brain-imaging techniques that revealed that the music caused dopamine peaks coupled with emotional arousal.
The release of dopamine during music explains why such a high value is put on it and why music can manipulate our emotions. The effect that music has on us is quite comparable to other pleasures. Some examples are the joy of eating food, sex, and other tangible rewards.
Music can quite literally move us or the chemicals in our brains. The fact that music can really give us a rush like sex does is incredible. Well, the sensation is released from the same part of the brain at least.