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MoS2 and related metal dichalcogenides (MoSe2, WS2, WSe2) are layered two-dimensional materials that are promising for nanoelectronics and spintronics. For instance, large spin-orbit coupling and spin splitting in the valence band of single layer (SL) MoS2 could lead to enhanced spin lifetimes and large spin Hall angles. Understanding the nature of the contacts is a critical first step for realizing spin injection and spin transport in MoS2. Here, we have investigated Co contacts to SL MoS2 and find that the Schottky barrier height can be significantly decreased with the addition of a thin oxide barrier (MgO). Further, we show that the barrier height can be reduced to zero by tuning the carrier density with back gate. Therefore, the MgO could simultaneously provide a tunnel barrier to alleviate conductance mismatch while minimizing carrier depletion near the contacts. Such control over the barrier height should allow for careful engineering of the contacts to realize spin injection in these materials.