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We report on the measurement of spin density matrix elements of the Λ(1520) in the photoproduction reaction γp→Λ(1520)K+, via its subsequent decay to K−p. The measurement was performed as part of the GlueX experimental program in Hall D at Jefferson Laboratory using a linearly polarized photon beam with Eγ=8.2GeV-8.8GeV. These are the first such measurements in this photon energy range. Results are presented in bins of momentum transfer squared, −(t−t0). We compare the results with a Reggeon exchange model and determine that natural exchange amplitudes are dominant in Λ(1520) photoproduction.