Inclusion Criteria:  Sign the informed consent form prior to entry into the study Male or female subject with age 40 years to 80 years at the time of signed consent Meets the MDS-PSP study group criteria for possible or probable progressive supranuclear palsy with Richardson syndrome (postural instability and falls with vertical ocular motor dysfunction) Presence of PSP symptoms for less than 4 years Score of <40 on the PSPRS-28 Ambulatory patients (with or without assistive device - no handheld help) and capable of performing study assessments/evaluations Subject has an identified, reliable, study partner (e.g., caregiver, family member, social worker, or friend) who can assist in assuring that the subject is able to travel to the required visits. Willing to provide the necessary blood samples  Exclusion Criteria:  Received treatment with other experimental therapies within the last 30 days prior to the first dose. The last dose of the prior experimental agent must have occurred more than 5 half-lives prior to enrollment in the current trial. Previously received treatment with RT001 Refusal to discontinue fish oils or other oil-based supplements for the duration of the study (Screening/Baseline till last study procedure completed) Mini mental state examination (MMSE) score less than 20 at screening Subject resides at a skilled nursing or dementia care facility, or admission to such a facility is planned during the study period Evidence of any clinically significant neurological disorder other than PSP in particular CBS Evidence of a clear and robust benefit from levodopa at the time of screening. Participants are permitted to take levodopa and other Parkinson's medications if the dose had been stable for 60 days prior to screening The subject has a history of or currently has schizophrenia, schizoaffective disorder or bipolar disorder according to DSM-V or ICD-10 criteria Subject has had a significant illness or infection requiring medical intervention in the past 30 days Subject has evidence of any disease or condition (based on either history, physical or laboratory values) that might interfere with the conduct of the study Is currently receiving active deep brain stimulation (DBS) that cannot be turned off Any condition with a life expectancy of less than 2 years Female who is breastfeeding or has a positive pregnancy test Male participant or female participant of childbearing potential, who is sexually active and unwilling/unable to use a highly effective birth control method throughout the study Unwilling or unable to comply with the requirements of this protocol, including the presence of any condition (physical, mental, or social) that is likely to affect the subject's ability to return for visits as scheduled History, within the last 2 years, of alcohol abuse or physical opioid dependence