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Decision support is the science and associated practice that consist in providing recommendations to decision makers facing problems, based on available theoretical knowledge and empirical data. Although this activity is often seen as being concerned with solving mathematical problems and conceiving algorithms, it is essentially an empirical and socially framed activity, where interactions between clients and analysts, and between them and concerned third parties, play a crucial role. Since the 80s, two concepts have structured the literature devoted to analysing this aspect of decision support: validity and legitimacy. Whereas validity is focused on the interactions between the client and the analyst, legitimacy refers to the broader picture: the organisational context, the overall problem situation, the environment, culture, history. Despite its importance, this concept has not received the attention it deserves in the literature in decision support. The present paper aims at filling this gap. For that purpose, we review the literature in other disciplines relevant to elaborate a concept of legitimacy useful in decision support contexts. Based on this review, we propose a general theory of legitimacy, adapted to decision support contexts, encompassing the relevant contributions we found in the literature. According to this general theory, a legitimate decision support intervention is one for which the decision support provider produces a justification that satisfies two conditions: (i) it effectively convinces the decision support provider's interlocutors (effectiveness condition) and (ii) it is organised around the active elicitation of as many and as diverse counterarguments as possible (truthfulness condition). Despite its conceptual simplicity, legitimacy, understood in this sense, is a very exacting requirement, opening ambitious research avenues that we delineate.