Psychedelics have a checkered past, alternately venerated as sacred medicines and vilified as narcotics with no medicinal or research value. After decades of international prohibition, a growing dissatisfaction with conventional mental health care and the pioneering work of the Multidisciplinary Association for Psychedelic Science (MAPS) and others has sparked a new wave of psychedelic research. Positive media coverage and new entrepreneurial interest in this potentially lucrative market, along with their attendant conflicts of interest, have accelerated the hype. Given psychedelics’ complex history, it is especially important to proceed with care, holding ourselves to a higher scientific rigor and standard of transparency. Universities and researchers face conflicting interests and perverse incentives, but we can avoid missteps by expecting rigorous and transparent methods in the growing science of psychedelics. This paper provides a pragmatic research checklist and discusses the importance of using the modern research and transparency standards of Open Science using preregistration, open materials and data, reporting constraints on generality, and encouraging replication. We discuss specific steps researchers should take to avoid another replication crisis like those devastating psychology, medicine, and other fields. We end with a discussion of researcher intention and the value of actively deciding to abide by higher scientific standards. We can build a rigorous, transparent, replicable psychedelic science by using Open Science to understand psychedelics’ potential as they re-enter science and society.