  In this paper, we present a foundation study for proper colouring of edge-set
graphs. The authors consider that a detailed study of the colouring of edge-set
graphs corresponding to the family of paths is best suitable for such
foundation study. The main result is deriving the chromatic number of the
edge-set graph of a path, $P_{n+1}$, $n \geq 1$. It is also shown that edge-set
graphs for paths are perfect graphs.
