Hundreds of Iraq and Afghanistan veterans with post-traumatic stress have recently contacted a husband-and-wife team who work in suburban South Carolina to seek help. Many are desperate, pleading for treatment and willing to travel to get it.

The soldiers have no interest in traditional talking cures or prescription drugs that have given them little relief. They are lining up to try an alternative: MDMA, better known as Ecstasy, a party drug that surfaced in the 1980s and ’90s that can induce pulses of euphoria and a radiating affection. Government regulators criminalized the drug in 1985, placing it on a list of prohibited substances that includes heroin and LSD. But in recent years, regulators have licensed a small number of labs to produce MDMA for research purposes.