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The discovery of superconductivity in magic angle twisted bilayer graphene has ignited great interest in exploring flat bands in two-dimensional van der Waals heterostructures. We demonstrate for the first time the existence of flat bands in the electronic structure of a 3° twisted bilayer WSe2 sample using low temperature scanning tunneling microscopy and spectroscopy. Using variable height spectroscopy, we observe sharp peaks in the density of states near the valence band edge related to the flat bands. By decay constant measurements, we assign various peaks in the density of states to different locations in the Brillouin zone. By direct spatial mapping of the wavefunctions at the flat band energy, we have found that the flat band is localized in the form of a hexagonal network, which is in excellent agreement with first-principle density functional theory calculations.