The electrical injection, transport and detection of spins in silicon is studied using non-local spin-transport devices with an n-type Si channel and Fe/MgO magnetic tunnel contacts. Clear spin-valve and Hanle spin signals with consistent magnitude are observed, unambiguously proving the existence of a spin accumulation in the Si channel. Importantly, the spin accumulation is very large, and increased by one to two orders of magnitude when compared to previous reports. We attribute this to the large tunnel spin polarization of the Fe/MgO contacts. Using devices with different growth procedures it is shown that the quality of the tunnel contacts and the magnitude of the non-local spin signals depend significantly on the details of the contact fabrication. The results demonstrate that a large spin accumulation can indeed be induced in Si, as is required for the development of Si spintronic devices with a large magnetic response.