The first classes at the UW Madison were held in the winter of 1849 and with an class of only 17 students, dormitories were not a pressing need. But, by just the next year, the Board of Regents had approved plans for the construction of the first dorms on campus, simply called North Hall (1851) and South Hall (1855). The units had outdoor privies and students had to bring water in from a nearby well, but they did have furnaces, which were so bad at heating the buildings that they were done away with within years, leaving the heating to fireplaces. There were no RAs, no sophisticated mechanisms for collecting fees and managing furniture. Those duties actually fell to the Dean of Faculty and Vice-Chancellor, John Sterling.
Once women were admitted to the University, South Hall became exclusively, though briefly dedicated to their housing; women were moved to the obviously named Ladies Hall in 1874. Ladies Hall was renamed Chadbourne Hall in 1901 for largely two reasons. First, Chancellor Paul Chadbourne had acquired the lot for the UW, but more interestingly, E.A. Birge thought, "it was only fair that Dr. Chadbourne's contumacy regarding coeducation should be punished by attaching his name to a building which turned out [to be] one of the main supports of coeducation." So, for those out there counting, Chadbourne Hall was the first (and perhaps only) dorm named to spite and honor the same man.
More early dorm history can be found in Barry Teicher's A History of Housing at the University of Wisconsin and there are pictures and postcards of dorm life throughout the UW Madison Collection.