Leber’s Hereditary Optic Neuropathy (LHON) appears as an enigmatic condition; affecting only certain families and often causing a severe loss of vision seemingly at random amongst family members. The first breakthrough came in 1988 with the linking of the condition to a mutation in the mitochondrial DNA (mtDNA). Now it is known that about 90% of cases are linked to 3 mutations. In this paper the hypothesis is suggested that a LHON mutation decreases the function of the mitochondrial enzyme, Complex I, by 50% and this alone critically endangers the survival of cells - especially the fragile cells of the optic nerves. A computer model has been written to illustrate how the hypothesis can produce a natural history for the condition of LHON that has features similar to those observed in practice; thereby successfully explaining the behaviour of this enigmatic condition.