This clinical trial will test a promising drug for treatment of long COVID in 300 adults who 1) are post-COVID-19 (at least 3 months since initial COVID symptoms and/or test confirming SARS-CoV-2 infection); and 2) have evidence of neurocognitive Long COVID (e.g., "brain fog", trouble concentrating, etc) which is causing suffering and/or impairment. The trial will determine whether fluvoxamine (1) reduces long COVID symptoms, 2) improves cognitive performance. Fluvoxamine is an SSRI (FDA approved for OCD) that also activates the sigma-1 receptor (an immunomodulatory receptor). It has been shown to prevent clinical deterioration and hospitalization in outpatients with acute COVID-19 (STOP COVID and TOGETHER trials). For the current study, we will randomize participants to fluvoxamine which is initially dosed at their preference, vs. placebo. This is done in the following manner. First, each participant will receive an acute bout of fluvoxamine: one dose of 25mg, then one dose of 50mg, then one dose of 100mg. We will assess their subjective reaction to these test doses and use the information to randomize them to an individually tailored course of fluvoxamine, vs. a matched placebo, for 16 weeks. The benefits of this are (1) participants are more likely to accept randomization and continue in the study if randomized to a dose they've already tested and accepted; (2) participants' initial response, if any, to the acute dose may allow future precision-medicine use of fluvoxamine, allowing physicians to give patients a test dose and then a full trial preferentially to participants who are likely to respond. After the randomized portion of the trial, participants will be given an opportunity to participate in open-label treatment with fluvoxamine for 16 weeks. At the end of treatment, the study medication will be tapered off over an approximate 1-2 week period, depending on the final dose of study medication, and adjusted as appropriate if they experience discontinuation symptoms. Outcome assessments will be a combination of patient-reported assessments and validated neuropsychological tests.