Inflammatory processes are important in the progressive loss of memory and thinking skills in Alzheimer's disease (AD). Laboratory studies show that drugs that bind to a protein known as "Peroxisome Proliferator Activated Receptor-gamma (PPARgamma)" act to reduce inflammatory responses in brain cells known as microglia when they are exposed to amyloid peptide, a major part of AD pathology. Therefore, drugs that activate PPARgamma have great potential for reducing the progression of AD. Pioglitazone (PGZ) activates PPARgamma and has shown favorable clinical experiences and safety profiles in patients with diabetes. This is a pilot study to determine the safety and tolerability of PGZ in patients with AD. Another goal of the study is to assess how clinical measures of cognition, daily function, and behavior might respond to PGZ treatment.