An effective and widely used vaccine could reduce the burden of dengue virus (DENV) worldwide. DENV is endemic in Puerto Rico, where the CYD-TDV dengue vaccine is currently being considered as a control measure. The CYD-TDV vaccine has demonstrated efficacy in clinical trials in vaccinated people who had a previous infection with the dengue virus. However, in vaccinated people who had no previous infection with the dengue virus, the vaccine posed a modestly high risk of hospitalization and serious illness. Therefore, the WHO recommended a screening strategy prior to vaccination and vaccination of HIV-positive people. To estimate the cost-effectiveness and benefits of this intervention (i.e., screening and vaccination of HIV-positive people) in Puerto Rico, we simulated 10 years of intervention in 9-year-old children using an agent-based model. Across the population, we found that 5.5% (4.6%-6.3%) of hospitalizations for dengue fever could be avoided. However, we also found that there could be 0.057 (0.045—0.073) additional hospitalizations per 1,000 people in Puerto Rico due to DENV-naïve children who were vaccinated after a false-positive result in the previous exposure test. The ratio between avoided hospitalizations among all those vaccinated and additional hospitalizations among those vaccinated naïve to DENV was estimated to be 19 (13—24). With a base vaccination cost of 382 USD, we found an incremental cost-effectiveness ratio of 122,000 USD per Quality Adjusted Years of Life (QALY) earned. Our estimates can provide information for considering the introduction of the CYD-TDV vaccine in Puerto Rico.