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The two-dimensional (2D) semiconductor molybdenum disulfide (MoS2) has attracted widespread attention for its extraordinary electrical, optical, spin and valley related properties. Here, we report on spin polarized tunneling through chemical vapor deposited (CVD) multilayer MoS2 (~7 nm) at room temperature in a vertically fabricated spin-valve device. A tunnel magnetoresistance (TMR) of 0.5 - 2 % has been observed, corresponding to spin polarization of 5 - 10 % in the measured temperature range of 300 - 75 K. First principles calculations for ideal junctions results in a tunnel magnetoresistance up to 8 %, and a spin polarization of 26 %. The detailed measurements at different temperatures and bias voltages, and density functional theory calculations provide information about spin transport mechanisms in vertical multilayer MoS2 spin-valve devices. These findings form a platform for exploring spin functionalities in 2D semiconductors and understanding the basic phenomenon that control their performance.