Depression is a leading cause of disability worldwide, in part because the available treatments are inadequate and do not work for many people. The neurobiology of depression, and the mechanism of action of common antidepressant drugs such as selective serotonin reuptake inhibitors (SSRIs), is not well understood. One mechanism thought to underlie the effects of these drugs is upregulation of adult hippocampal neurogenesis. Evidence indicates that vesicular zinc is required for modulation of adult hippocampal neurogenesis, at least under some circumstances. Vesicular zinc refers to zinc that is stored in the synaptic vesicles of certain neurons, including in the hippocampus, and released in response to neuronal activity. It can be eliminated from the brain by deletion of zinc transporter 3 (ZnT3), as is the case in ZnT3 knockout mice. Here, we examined the effects of repeated social defeat stress and subsequent chronic treatment with the SSRI fluoxetine on behavior and neurogenesis in ZnT3 knockout mice. We hypothesized that fluoxetine treatment would increase neurogenesis and reverse stress-induced behavioral symptoms in wild type, but not ZnT3 knockout, mice. As anticipated, stress induced persistent depression-like effects, including social avoidance and anxiety-like behavior. Fluoxetine decreased social avoidance, though the effect was not specific to the stressed mice, but did not affect anxiety-like behavior. Surprisingly, stress increased the survival of neurons born 1 day after the last episode of defeat stress. Fluoxetine treatment also increased cell survival, particularly in wild type mice, though it did not affect proliferation. Our results did not support our hypothesis that vesicular zinc is required for the behavioral benefits of fluoxetine treatment. As to whether vesicular zinc is required for the neurogenic effects of fluoxetine, our results were inconclusive, warranting further investigation into the role of vesicular zinc in adult hippocampal neurogenesis.