During the slow neutron capture process in massive stars, reactions on light elements can both produce and absorb neutrons thereby influencing the final heavy element abundances. At low metallicities, the high neutron capture rate of $^{16}$O can inhibit s-process nucleosynthesis unless the neutrons are recycled via the $^{17}$O(α,n)$^{20}$Ne reaction. The efficiency of this neutron recycling is determined by competition between the $^{17}$O(α,n)$^{20}$Ne and $^{17}$O(α,γ)$^{21}$Ne reactions. While some experimental data are available on the former reaction, no data exist for the radiative capture channel at the relevant astrophysical energies.The $^{17}$O(α,γ)$^{21}$Ne reaction has been studied directly using the DRAGON recoil separator at the TRIUMF Laboratory. The reaction cross section has been determined at energies between 0.6 and 1.6 MeV Ecm, reaching into the Gamow window for core helium burning for the first time. Resonance strengths for resonances at 0.63, 0.721, 0.81 and 1.122 MeV Ecm have been extracted. The experimentally based reaction rate calculated represents a lower limit, but suggests that significant s-process nucleosynthesis occurs in low metallicity massive stars.