Levetiracetam for Persons at Risk for Alzheimer's Disease

Inclusion Criteria: * Willing to undergo all study procedures and has signed the informed consent form * Within normal limits on the Montreal Cognitive Assessment (MoCA) at Screening * Age 55-85 * Female participants must be post-menopausal (amenorrheic for at least 12 consecutive months without other known or suspected cause) or surgically sterile (bilateral tubal ligation, total hysterectomy, or bilateral oophorectomy) * Sufficiently fluent in English to undergo cognitive testing, per investigator judgment * Increased risk of Alzheimer's disease, as indicated by one or more of the following: 1. Participant has subjective cognitive complaints AND a family history of Alzheimer's disease (or of dementia suggestive of possible or probable Alzheimer's disease) in a first-degree relative; and/or 2. Participant is known to be amyloid or tau positive; and/or 3. Participant is known to be an APOE e4/e4 homozygote * Hippocampal hyperactivation, defined as activation \>1.5 MAD above the median, during the pattern separation task (PST) on BOLD fMRI. Exclusion Criteria: * History of hypersensitivity to levetiracetam or any other ingredients in the study drug or placebo. * Significant neurological disease, including but not limited to: 1. Any type of cognitive impairment 2. History of transient ischemic attacks within 12 months of Screening 3. History of seizures within 12 months of Screening 4. Epilepsy 5. Parkinson's disease 6. Stroke (aside from subcortical lacunar infarcts) 7. Multiple sclerosis 8. Huntington's disease 9. Normal pressure hydrocephalus 10. Brain tumour (aside from benign tumours without mass effect, which are to be judged on a case-by-case basis) 11. Subdural hematoma 12. History of traumatic brain injury with persistent neurological deficits 13. Known structural brain abnormalities * Significant or unstable psychiatric disease, including but not limited to: 1. Schizophrenia 2. Bipolar disorder 3. Major depression which is not controlled in the opinion of the investigator 4. Score ≥10 on the Geriatric Depression Scale (GDS) at Screening 5. Presence of active suicidal ideation within the last 3 months as indicated by "yes" response to Question 4 or 5 on the Suicidal Ideation portion of the C-SSRS at Screening 6. Answered "yes" to any of the suicide-related behaviours within the last 3 months on the Suicidal Behavior portion of the C-SSRS 7. Hospitalized or treated for suicidal behavior within 5 years of Screening 8. Psychotic features, agitation, or behavioral problems within the last 3 months that could lead to difficulty complying with the protocol in the opinion of the investigator * Known or suspected history of drug or alcohol abuse or dependence within 2 years before Screening). * Significant or unstable systemic illness or medical condition that would in the investigator's judgment make the participant unsuitable for inclusion in the study, including but not limited to: 1. History of malignancy within 3 years of screening (except of basal or squamous cell carcinoma of the skin) 2. Moderate-severe chronic kidney disease, chronic obstructive pulmonary disease, or congestive heart failure * Any of the following findings on a current (completed during screening) or previous brain MRI/CT scan: 1. Severe white matter disease (Fazekas score66 = 3) 2. Stroke involving a major vascular territory 3. Subcortical lacunar infarcts \>1.5cm in diameter 4. Encephalomalacia 5. Vascular malformations that are at high risk of hemorrhage 6. Infective lesions 7. Space-occupying lesions 8. Any other abnormality that would in the opinion of the investigator make the participant unsuitable for participation in the study * Any contraindications to MRI or MEG (e.g., pacemaker, ferromagnetic metal implants, claustrophobia). * Treatment with the following medications at time of screening or while in the study: 1. Anticonvulsant medications (unless taken for a different indication than seizures) 2. Methotrexate * eGFR \<50ml/min/1.73m2 on screening bloodwork. * QTc interval \>470 msec (males) or \>480 msec (females) on screening ECG. * Clinically significant abnormal results on screening bloodwork that would in the opinion of the investigator make the participant unsuitable for inclusion in the study.