We examine the prevalence and sources of student anxiety during the rise of the COVID-19 pandemic (March 23 to May 10, 2020) and the implications for online course design and delivery. Using a standard screening tool (GAD-7) with supplemental open-response questions, we show that students had relatively high levels of anxiety based on a convenience sample of 266 undergraduate students enrolled at four U.S. institutions. In this sample, we find that 58 percent of students had clinically significant levels of anxiety in one or more weeks of the seven-week study period. Thirty-six percent of students sustained this level of anxiety on average over the entire period. These rates are high compared to published rates for the general population (1.6 percent to 8.5 percent) and even among college students (17 percent to 40 percent). Using content analysis, we identify five primary sources of student anxiety: traditional academic concerns (72 percent), online learning (67 percent), general uncertainty (38 percent), health and safety (27 percent), and financial issues (12 percent). We similarly identify four ways that students say instructors can help them reduce their anxiety: improve the course structure and organization (36 percent), improve communication (35 percent), improve course materials and assignments (33 percent), and continue expressions of care and support (27 percent). Finally, we look at how these four student recommendations connect more broadly to (1) the published academic literature, (2) our own experiences as instructors, and (3) suggestions from other practitioners.