Eliciting, understanding, and honoring patients' values--the things most important to them in daily life--is a cornerstone of patient-centered care. However, this rarely occurs explicitly as a routine part of clinical practice. This is particularly problematic for individuals with multiple chronic conditions (MCC) because they face difficult choices about how to balance competing demands for self-care in accordance with their values. In this study, we sought to inform the design of interventions to support conversations about patient values between patients with MCC and their health care providers. We conducted a field study that included observations of 21 clinic visits for patients who have MCC, and interviews with 16 care team members involved in those visits. This paper contributes a practice-based account of ways in which providers engage with patient values, and discusses how future work in interactive systems design might extend and enrich these engagements.