Clinical Pharmacology of p38 MAP Kinase Inhibitor, VX-745, in Mild Cognitive Impairment Due to Alzheimer's Disease (AD) or Mild AD

Inclusion Criteria: * Age 60 - 85 (inclusive) * Willing and able to provide informed consent * Clinical presentation consistent with MCI due to AD or of mild AD * Gradual progressive decline in memory function over \>6 months * Amnestic presentation on neuropsychological testing with rapid forgetting (% reduction 1.5 standard deviations below the mean) * Clinical Dementia Rating (CDR) Sum of Box (SOB) score ≥0.5 * Mini-Mental State Examination (MMSE) range: 20 to 30 * Brain hypometabolism by 18F-2-fluoro-2-deoxyglucose (FDG)-PET * Participants may be taking medications for AD, provided that the dose of these medications has been stable for \>3 months. Exclusion Criteria: * Evidence of neurodegenerative disease other than AD * Inability for any reason to undergo MRI scans (e.g. pacemaker, vascular stent or stent graft). Patients who require sedation for screening procedures such as MRI may receive a short-acting sedative. * Psychiatric disorder that would compromise ability to comply with study requirements * History of cancer within the last 5 years, except basal cell carcinoma, non-squamous skin carcinoma, prostate cancer or carcinoma in situ with no significant progression over the past 2 years * Significant cardiovascular, pulmonary, renal, liver, infectious disease, immune disorder or metabolic/endocrine disorders or other disease that would preclude treatment with p38 MAP kinase inhibitor and/or assessment of drug safety and efficacy * Recent (\<90 days) changes to AD medications prescribed for cognitive reasons or with the potential to impact cognition * Psychotropic drugs taken within 1 month. Anticoagulant drugs taken within 1 week. * Participation in a study of an investigational drug less than 6 months or 5 half-lives of the investigational drug, whichever is longer, before enrollment in the study * Male subjects with female partner of child-bearing potential who are unwilling or unable to adhere to contraception requirements * Female subjects who have not reached menopause or have not had a hysterectomy or bilateral oophorectomy/salpingoophorectomy * Positive urine or serum pregnancy test or plans desires to become pregnant during the course of the trial * Donation of \>500 mL of blood or blood products within 2 months * History of alcohol and/or illicit drug abuse within 6 months. * Infection with hepatitis A, B or C or HIV. * Any factor deemed by the investigator to be likely to interfere with study conduction