On March 27, 2020, a University of Texas at Austin student with cough, sore throat, and shortness of breath had a positive test result for SARS-CoV-2, the virus that causes coronavirus disease 2019 (COVID-19). On March 28, two more symptomatic students had positive test results, alerting the COVID-19 Center at the University of Texas Health Austin (UTHA) to a potential outbreak; the center initiated an outbreak investigation the same day. UTHA conducted contact tracing, which linked the students' infections to a spring break trip to Cabo San Lucas, Mexico, during March 14-19. Among 231 persons tested for SARS-CoV-2 in this investigation, 64 (28%) had positive test results, including 60 (33%) of 183 Cabo San Lucas travelers, one of 13 (8%) household contacts of Cabo San Lucas travelers, and three (9%) of 35 community contacts of Cabo San Lucas travelers. Approximately one fifth of persons with positive test results were asymptomatic; no persons needed hospitalization, and none died. This COVID-19 outbreak among a young, healthy population with no or mild symptoms was controlled with a coordinated public health response that included rapid contact tracing and testing of all exposed persons. A coordinated response with contact tracing and testing of all contacts, including those who are asymptomatic, is important in controlling future COVID-19 outbreaks that might occur as schools and universities consider reopening.