Coronavirus disease-19 (COVID-19), caused by the SARS-CoV-2 virus, leads primarily to respiratory symptoms that can be fatal, particularly in at risk individuals. However, neurological symptoms have also been observed in patients, including headache, seizures, stroke, and fatigue. The cause of these complications is not yet known, and whether they are due to a direct infection of neural cells, such as neurons and astrocytes, or through indirect effects on supportive brain cells, is unknown. Here, we use brain organoids to examine SARS-CoV-2 neurotropism. We examine expression of the key viral receptor ACE2 in single-cell RNA sequencing (scRNA-seq) revealing that only a subset of choroid plexus cells but not neurons or neural progenitors express this entry factor. We then challenge organoids with both SARS-CoV-2 spike protein pseudovirus and live virus to demonstrate high viral tropism for choroid plexus epithelial cells but not stromal cells, and little to no infection of neurons or glia. We find that infected cells of the choroid plexus are an apolipoprotein and ACE2 expressing subset of epithelial barrier cells. Finally, we show that infection with live SARS-CoV-2 leads to barrier breakdown of the choroid plexus. These findings suggest that neurological complications may result from effects on the choroid plexus, an important barrier that normally prevents entry of immune cells and cytokines into the cerebrospinal fluid (CSF) and brain.