Trust is an important component of human-AI relationships and plays a major role in shaping the reliance of users on online algorithmic decision support systems. With recent advances in natural language processing, text and voice-based conversational interfaces have provided users with new ways of interacting with such systems. Despite the growing applications of conversational user interfaces (CUIs), little is currently understood about the suitability of such interfaces for decision support and how CUIs inspire trust among humans engaging with decision support systems. In this work, we aim to address this gap and answer the following question: to what extent can a conversational interface build user trust in decision support systems in comparison to a conventional graphical user interface? To this end, we built a text-based conversational interface, and a conventional web-based graphical user interface. These served as the means for users to interact with an online decision support system to help them find housing, given a fixed set of constraints. To understand how the accuracy of the decision support system moderates user behavior and trust across the two interfaces, we considered an accurate and inaccurate system. We carried out a 2 × 2 between-subjects study (N = 240) on the Prolific crowdsourcing platform. Our findings show that the conversational interface was significantly more effective in building user trust and satisfaction in the online housing recommendation system when compared to the conventional web interface. Our results highlight the potential impact of conversational interfaces for trust development in decision support systems.