Astronomy arises very early in a civilisation and evolves as the civilisation advances. It is therefore reasonable to assume that a vibrant knowledge of astronomy would have been a feature of a civilisation the size of the Harappan Civilisation. We suggest that structures dedicated to astronomy existed in every major Harappan city. One such city was Dholavira, an important trading port that was located on an island in what is now the Rann of Kutch during the peak of the Harappan Civilisation. We have analysed an unusual structure at Dholavira that includes two circular rooms. Upon assuming strategically-placed holes in their ceilings we examine the internal movement of sunlight within these rooms and suggest that the larger structure of which they formed a part could have functioned as an astronomical observatory.