A large exchange splitting of the conduction band in ultrathin films of the ferromagnetic semiconductor EuO was determined quantitatively, by using EuO as a tunnel barrier and fitting the current-voltage characteristics and temperature dependence to tunneling theory. This exchange splitting leads to different tunnel barrier heights for spin-up and spin-down electrons and is large enough to produce a near-fully spin-polarized current. Moreover, the magnetic properties of these ultrathin films (<6 nm) show a reduction in Curie temperature with decreasing thickness, in agreement with theoretical calculation [R. Schiller, Phys. Rev. Lett. 86, 3847 (2001)10.1103/Phys. Rev. Lett.86.3847].