An Investigation of Psilocybin on Behavioural and Cognitive Symptoms of Adults With Fragile X Syndrome

Inclusion Criteria: 1. 18 to 50 years of age 2. BMI \> 18.3 3. Diagnosis of Fragile X syndrome with a molecular genetic confirmation of the full FMR1 mutation (\>200 CGG repeats) or the other loss of function mutations of the FMR1 gene (SNVs and deletions of the gene) based on evidence provided by caregiver from prior assessment 4. IQ between 40 and 85 points as reported by caregiver based on prior assessment 5. Subject has the ability to understand and provides voluntary, written, informed consent to participate in the study Or, For subjects who are not their own legal guardian, or do not have the capacity to provide informed consent, subject's parent/legal authorized guardian is able to understand and sign an informed consent form to participate in the study. 6. Caregiver (parent, guardian, or other legally authorized representative) who is willing to participate in the whole study and provides informed consent 7. Subject is able to swallow tablets and capsules 8. Individual is not of child-bearing potential, defined as those who have undergone a sterilization procedure (e.g. hysterectomy, bilateral oophorectomy, bilateral tubal ligation, complete endometrial ablation) or have been post-menopausal for at least 1 year prior to screening Or, Individuals of child-bearing potential must have a negative baseline urine pregnancy test and agree to use a medically approved method of birth control for the duration of the study. All hormonal birth control must have been in use for a minimum of three months. Acceptable methods of birth control include: * Abstinence (only in cases when abstinence is the usual and customary form of birth control for the participant) * Hormonal contraceptives including oral contraceptives, hormone birth control patch (Ortho Evra), vaginal contraceptive ring (NuvaRing), injectable contraceptives (Depo-Provera, Lunelle), or hormone implant (Norplant System) * Double-barrier method * Intrauterine devices * Non-heterosexual lifestyle or agrees to use contraception if planning on changing to heterosexual partner(s) * Vasectomy of partner at least 6 months prior to screening Exclusion Criteria: 1. Individuals who are pregnant, breast feeding, or planning to become pregnant during the study 2. Allergy, sensitivity, or intolerance to the investigational product's active or inactive ingredients 3. Regular use of medications that may have problematic interactions with psilocybin, including but not limited to dopamine agonists, MAO inhibitors, N-methyl-D-aspartate (NMDAR) antagonists, antipsychotics, and stimulants 4. Urine drug test containing non-prescribed drugs of abuse (non-prescribed opioids, benzodiazepines, amphetamines, phencyclidine, cocaine) at screening and day of first treatment. Urine cannabinoid concentrations \>50 ng/ml will suggest heavy marijuana use and will be a threshold for excluding potential subjects 5. Having uncontrolled hypertension defined as an average systolic blood pressure ≥140 mmHg or an average diastolic blood pressure ≥90 mmHg, with at least 4 BP assessments completed. 6. Have any of the following cardiovascular conditions: coronary artery disease, congenital long QT (time from the start of the Q wave to the end of the T wave) syndrome, cardiac hypertrophy, cardiac ischemia, congestive heart failure, myocardial infarction, tachycardia, artificial heart valve, a clinically significant screening ECG abnormality, or any other significant cardiovascular condition 7. Significant cardiovascular event in the past 6 months. Participants with no significant cardiovascular event on stable medication may be included after assessment by the QI on a case-by-case basis 8. Subjects with a history of seizure disorder except those who are currently receiving treatment with anti-epileptics and have been seizure-free for 3 months preceding screening or have been seizure-free for 3 years if not currently receiving anti-epileptics. 9. Reported history of moderate to severe hepatic impairment 10. Type I or insulin-dependent Type II diabetes 11. Meet DSM-5 criteria for schizophrenia spectrum or other psychotic disorders, including major depressive disorder with psychotic features, or Bipolar I or Bipolar II Disorder 12. Meet DSM-5 criteria for a moderate or severe alcohol or drug use disorder in the past 12 months 13. Subjects who plan to initiate or change pharmacologic or non-pharmacologic interventions during the course of the study 14. Medical illness based on physical examination, ECG and routine testing that may complicate cardiovascular safety or drug metabolism or excretion, such as metabolic disease, severe cardiac disease, or kidney or liver failure as assessed by the QI. QI assessments will be based on clinical history provided by caregivers and/or physicians. Any participant requiring further assessment will be referred accordingly or excluded by the QI on a case-by-case basis.\* 15. Current or history of any significant diseases of the gastrointestinal tract, exceptions to be determined by the QI 16. Unstable hypertension. Treatment on a stable dose of medication for at least 3 months will be considered by the QI on a case-by-case basis 17. Major surgery in the past 3 months or individuals who have planned surgery during the course of the study. Participants with minor surgery will be considered on a case-by-case basis by the QI 18. Participation in other clinical research studies 30 days prior to enrollment as assessed by the QI. 19. Any other condition or lifestyle factor, that, in the opinion of the QI, may adversely affect the participant's ability to complete the study or its measures or pose significant risk to the participant \* Blood draw to obtain laboratory samples for analysis will be avoided in this study due to the undue stress it places on this clinical population and the high safety profile of the medication at the dosage being used.