We answer a 1975 question of G R Gordh by showing that if X is a homogeneous compactum which is the continuous image of a compact ordered space then at least one of the following holds
(I) X is metrizable, (II) dim X = 0 or (III) X is a union of finitely many pairwise disjoint generalized simple closed curves.
We begin to examine the structure of homogeneous 0-dimensional spaces which are continuous images of ordered compacta.