A hypothesis, and one that's in some amount of shadow right now. Work published within the last year by Hans Thewissen and his group suggest that whales are more closely related to hippopotami - molecular data had already suggested that.
http://www.neoucom.edu/Depts/Anat/whaleorigins.htmhas some details.
I guess Tr/O needs an updated article. I wouldn't call the whale-mesonychian hypothesis a "conjecture," though. There appears to have been a lot of fossil data backing it up, but the new fossils Thewissen found provided new data, which better support a hippo relationship.
Edited to add:
Indiana University Bloomingtonhas bunches of stuff, with links.
[This message has been edited by Coragyps, 11-23-2002]