The Chariot Races first started as part of the Engineering Society elections in 1912.
In the early days Society elections were held in the evening, and after the voting the participants would pile all the drafting tables in a corner of the first-year drafting room. This mammoth room was located on the third floor of the litte red Schoolhouse. Everyone wore old clothes suitable for the celebrations, and indoor football, broomball, and chariot races ensued. In these early chariot races, each aspiring Ben Hur balanced himself on a thunder pot whose handle was threaded with tow-ropes. Fleet-footed Schoolmen would propel the chariots around the improvised coliseum to the wild cheering of the crowd. MacElhinney (1973), p. 32-33.
They are further mentioned, in less colourful terms, in both 1913 and 1915, where they are referred to as the chariot race but no mention is made of the structure of the chariots.
One of the important events among the former was a chariot race which will long be remembered for its uniqueness and for its close finish, taxing the capabilities of the judges to the elastic limit. Irwin (1913), p.4
The next event, a modern chariot race, in which a team of seven men from each year was entered, was perhaps the most interesting and lively of the evening. Ritchie (1915), p.2.
While Monday, February 2, 1947, is often viewed as the first time the chariot races were opened up to other faculties, this may not be the full story as the rivalry with Medicine manifests in the 1930s with a chariot race (or two) as well and still continues into the 1940s, even with the inclusion of other faculties.