Zirconium carbide has a wide range of stoichiometry facilitated by carbon vacancies. Vacancy-ordered zirconium carbide phases have been intermittently observed at low temperatures for decades, but prove challenging to reliably fabricate or characterise. Theoretical predictions suggest that a series of ordered ZrCx phases should precipitate as a function of vacancy content, being significantly more stable than the more-observed vacancy-disordered phase. In experimental samples, it is very common to have significant oxygen impurities which may affect the properties and structure. Using first-principles calculations, the stability of the vacancy-ordered and -disordered phases is investigated as function of oxygen defect concentration at various sites in the ZrCx structures. The calculations show that the relative stability of the ordered phases decreases with increasing oxygen content, and there is a threshold oxygen level beyond which the vacancy-disordered phase is stabilised. This threshold oxygen content is less than is often present in experimental samples of zirconium carbide, which may explain why such phases are rarely reported.