Kilmer entered Rutgers College Grammar School (now Rutgers Preparatory School) in 1895 at the age of 8. During his years at the Grammar School, Kilmer was editor-in-chief of the school's paper, the "Argo", and loved the classics but had difficulty with Greek. He won the first Lane Classical Prize, for oratory, and obtained a scholarship to Rutgers College which he would attend the following year. Despite his difficulties with Greek and mathematics, he stood at the head of his class in preparatory school.