Ubiquitin mediated proteolysis is required for transition from one cell cycle phase to another. For instance, the mitosis inhibitor Wee1 is targeted for degradation during S phase and G2 to allow mitotic entry. Wee1 is an essential tyrosine kinase required for the G2/M transition and S-phase progression. Although several studies have concentrated on Wee1 regulation during mitosis, few have elucidated its degradation during interphase. Our prior studies have demonstrated that Wee1 is degraded via CK1δ dependent phosphorylation during the S and G2/M phases of the cell cycle. Here we demonstrate that GSK3β may work in concert with CK1δ to induce Wee1 destruction during interphase. We generated small molecules that specifically stabilized Wee1. We profiled these compounds against 296 kinases and found that they inhibit GSK3α and GSK3β, suggesting that Wee1 may be targeted for proteolysis by GSK3. Consistent with this notion, known GSK3 inhibitors stabilized Wee1 and GSK3β depletion reduced Wee1 turnover. Given Wee1's central role in cell cycle progression, we predicted that GSK3 inhibitors should limit cell proliferation. Indeed, we demonstrate that GSK3 inhibitors potently inhibited proliferation of the most abundant cell in the mammalian brain, the cerebellar granule cell progenitor (GCP). These studies identify a previously unappreciated role for GSK3β mediated regulation of Wee1 during the cell cycle and in neurogenesis. Furthermore, they suggest that pharmacological inhibition of Wee1 may be therapeutically attractive in some cancers where GSK-3β or Wee1 are dysregulated.