Palmer was born in Cedar Falls, Iowa, and graduated from the University of Illinois in 1919 with a degree in architecture. He moved to Oak Park, Illinois in 1921 and became involved in the Prairie school movement. He worked for Frank Lloyd Wright for a short time before opening his own practice in 1922.
Palmer's designs were influenced by Wright, but he also developed his own unique style. He was known for his use of simple forms, natural materials, and open floor plans. He also frequently incorporated elements of nature into his designs, such as gardens, terraces, and pools.
Palmer designed over 1,000 homes and other buildings during his career. Many of his works are located in the Chicago area, but he also designed projects in other parts of the United States and Canada. Some of his most notable works include the Palmer House (1927), the Winnetka Community House (1928), and the Chicago Botanic Garden (1940).
Palmer was also a professor of architecture at the Illinois Institute of Technology from 1945 to 1968. He was a Fellow of the American Institute of Architects and received numerous awards for his work, including the AIA Gold Medal in 1967.
Palmer died in Oak Park, Illinois, in 1978. His legacy continues through his work, which is considered to be some of the best examples of Prairie school architecture.