In 1949, Chiume went to Makerere College in Kampala, Uganda, the premier university in East Africa, and in 1951 he was admitted into Makerere College's Medicine School. He later changed his major to Education, after discovering that he "could not stand human dissection", specializing in Physics, Chemistry and Biology. Among his contemporaries at Makerere were people who would in later life become some of Africa's most accomplished scholars and public officials, including B. Ogot, Kenya's celebrated historian and Chancellor of Moi University in Eldoret, and the second Kenyan president Mwai Kibaki. He was president of the Makerere College Political Society, while Mwai Kibaki was a committee member. Later he was joined at Makerere by other Nyasas, Vincent Gondwe, David Rubadiri (former Vice Chancellor of the University of Malawi), and Augustine Bwanausi (former Malawi cabinet minister). Chiume was also chairperson of the Makerere College Education Society. Chiume and other students formed a Nyasaland Students Association at Makerere, an association that helped the Nyasaland African Congress by doing research, and by also linking up with fellow Nyasas at Fort Hare College, where Henry Masauko Chipembere, a lifelong friend and political colleague of Chiume's, went for his own university education. Another future leader of Nyasa nationalism, Dunduzu Chisiza, was also active in the Nyasaland Students Association at this time.