Which drug is a well-known narcotic analgesic?

Codeine is a well-known narcotic analgesic because it is an opioid medication that is primarily used to relieve mild to moderate pain. As part of the opioid class, it acts by binding to specific receptors in the brain and spinal cord, decreasing the perception of pain and providing relief.

In contrast to other options, Valium is a benzodiazepine used mainly for anxiety and muscle spasms, while Secobarbital is a barbiturate primarily prescribed for insomnia and sedation rather than pain relief. Meth, often referring to methamphetamine, is a powerful stimulant with little to no analgesic properties and is not used for pain management. Thus, codeine is the clear answer as it is designated for its analgesic, or pain-relieving, properties.