镇痛剂 (zhèntòngjì): painkiller

镇 'suppress' + 痛 'pain' + 剂 'agent/preparation' — literally 'pain-suppressing agent'. The 剂 suffix marks medical/chemical preparations: 麻醉剂 (mázuìjì) anesthetic, 防腐剂 (fángfǔjì) preservative.

usage

止痛药 (zhǐtòngyào) is the everyday spoken word for the same thing. 镇痛剂 sounds more clinical/technical — what you'd see in a medical context or product description.