The Checkered Chariot is a standard checker taxi cab. The checker or chess board pattern is connected to Freemasonry because it is found on the floor of Masonic Temples and Tracing Boards. The taxi cab, when combined with the checkered pattern, becomes a sort of "Chariot of the Gods," and is usually found carrying the protagonist in a movie. A cars power is measured in "horse power," which also brings in the idea of a chariot. Checkered cabs are typical and movies based in large cities such as New York.
The checker chariot is connected to the Chariot card of the Rider Waite Tarot deck which features a chariot pulled by black and white sphinxes, reminiscent of the checkered pattern seen on the cabs. In Crowley's Thoth deck, the charioteer carries the Holy Grail.