This resolves to Vox Future Perfect's judgement of this question.

After publishing some promising study results, the Multidisciplinary Association for Psychedelic Studies (MAPS) recently filed for FDA approval of MDMA-assisted therapy for PTSD. Now the two questions are: Will the FDA grant its approval, and if so, will it do so by the end of 2024?

For my prediction to come true, we need a “yes” to both. I am pretty confident MDMA will get the green light because in addition to the strong study results (and MAPS and the FDA agreed in advance on the study design), there is now robust public support for trying innovative methods to help people with mental health issues. A 2022 letter from the Health and Human Services Department disclosed that President Biden’s administration anticipates regulators will approve MDMA for PTSD and psilocybin for depression within the next two years.

But the FDA is, um, not exactly known for speed. If it views the MAPS filing as complete, it will aim to render a decision in six to 10 months. But because this is a psychedelic drug we’re talking about, we may see extra risk evaluations, which could drag out the timeline. So although I think approval is likely in late 2024, I won’t give this prediction more than 85 percent odds. —SS

Vox's prediction was "85 percent"