Highly frustrated systems have macroscopically degenerate ground states that lead to novel properties. In magnetism its consequences underpin exotic and technologically important effects, such as, high temperature superconductivity, colossal magnetoresistence, and the anomalous Hall effect. One of the enduring mysteries of frustrated magnetism is why certain experimental systems have a spin glass transition and its exact nature, given that it is not determined by the strength of the dominant magnetic interactions. There have been some suggestions that real systems possess disorder of the magnetic sites or bonds that are responsible. We show that the spin glass transition in the model kagome antiferromagnet hydronium jarosite arises from a spin anisotropy. This weaker energy scale is much smaller than that of the magnetic exchange, yet it is responsible for the energy barriers that are necessary to stabilise a glassy magnetic phase at finite temperature. The resultant glassy phase is quite unlike those found in conventional disordered spin glasses as it is based on complex collective rearrangements of spins called "spin folds". This simplifies hugely theoretical treatment of both the complex dynamics characteristic of a spin glass and the microscopic nature of the spin glass transition itself.