Yesterday a trip to the web site for the Department of Physics eventually led me to the Wikipedia entry for Lars Onsager, a former member of the Department of Chemistry. Here's the first paragraph from the section on his time at Yale:

At Yale, an embarrassing situation occurred: he had been hired as a postdoctoral fellow, but it was discovered that he had never received a Ph. D. While he had submitted an outline of his work in reciprocal relations to the Norwegian Institute of Technology, they had decided it was too incomplete to qualify as a doctoral dissertation. He was told that he could submit one of his published papers to the Yale faculty as a dissertation, but insisted on doing a new research project instead. His dissertation, entitled, "Solutions of the Mathieu equation of period 4 pi and certain related functions", was beyond the comprehension of the chemistry and physics faculty, and only when some members of the mathematics department, including the chairman, insisted that the work was good enough that they would grant the doctorate if the chemistry department would not, was he granted a Ph. D. in chemistry in 1935. Even before the dissertation was finished, he was appointed assistant professor in 1934, and promoted to associate professor in 1940. He quickly showed at Yale the same traits he had at JHU and Brown: he produced brilliant theoretical research, but was incapable of giving a lecture at a level that a student (even a graduate student) could comprehend. He was also unable to direct the research of graduate students, except for the occasional outstanding one.

Onsager was awarded the Nobel Prize in Chemistry in 1968.