Chase was born in Ann Arbor, Michigan, in 1856. His father, John Manley Chase, was a New York native and a civil engineer who surveyed the site of Lansing, Michigan, and served as one of the first treasurers of the University of Michigan. His mother was Elvira L (Ludden) Chase. At the time of the 1860 United States Census, Chase lived with his parents and two older siblings in Ann Arbor. His father's occupation was listed at the time as a farmer, and the value of his real estate was listed as $5,000. Chase was educated in the Ann Arbor public schools and graduated from Ann Arbor High School in 1875.