Virtual reality biofeedback systems for relaxation training can be an effective tool for reducing stress and anxiety levels, but most of them offer a limited user experience associated to the execution of a single task and a biofeedback mechanism that reflects a single physiological measurement. Furthermore, user evaluations of such systems do not typically include a placebo condition, making it difficult to determine the actual contribution of biofeedback. This paper proposes a VR system for breathing and relaxation training that: (i) uses biofeedback mechanisms based on multiple physiological measurements, (ii) provides a richer user experience through a narrative that unfolds in phases where the user is the main character and controls different elements of the virtual environment through biofeedback. To evaluate the system and to assess the actual contribution of biofeedback, we compared two conditions involving 35 participants: a biofeedback condition that exploited real-time measurements of user's breathing, skin conductance, and heart rate; and a placebo control condition, in which changes in the virtual environment followed physiological values recorded from a session with another user. The results showed that the proposed virtual experience helped users relax in both conditions, but real biofeedback produced results that were superior to placebo biofeedback, in terms of both relaxation and sense of presence. These outcomes highlight the important role that biofeedback can play in virtual reality systems for relaxation training, as well as the need for researchers to consider placebo conditions in evaluating this kind of systems.