We propose to create a secondary beam of neutral kaons in Hall D at Jefferson Lab to be used with the GlueX experimental setup for strange hadron spectroscopy. A flux on the order of 3 x 10^4 KL/s will allow a broad range of measurements to be made by improving the statistics of previous data obtained on hydrogen targets by three orders of magnitude. Use of a deuteron target will provide first measurements on the neutron which is {it terra incognita}. The experiment will measure both differential cross sections and self-analyzed polarizations of the produced {Lambda}, {Sigma}, {Xi}, and {Omega} hyperons using the GlueX detector at the Jefferson Lab Hall D. The measurements will span c.m. cos{theta} from -0.95 to 0.95 in the c.m. range above W = 1490 MeV and up to 3500 MeV. These new GlueX data will greatly constrain partial-wave analyses and reduce model-dependent uncertainties in the extraction of strange resonance properties (including pole positions), and provide a new benchmark for comparisons with QCD-inspired models and lattice QCD calculations. The proposed facility will also have an impact in the strange meson sector by providing measurements of the final-state K{pi} system from threshold up to 2 GeV invariant mass to establish and improve on the pole positions and widths of all K*(K{pi}) P-wave states as well as for the S-wave scalar meson {kappa}(800).