  We report the high-field superconducting properties of thin, disordered Re
films via magneto-transport and tunneling density of states measurements. Films
with thicknesses in the range of 9 nm to 3 nm had normal state sheet
resistances of $\sim$0.2 k$\Omega$ to $\sim$1 k$\Omega$ and corresponding
transition temperatures in the range of 6 K to 3 K. Tunneling spectra were
consistent with those of a moderate coupling BCS superconductor.
Notwithstanding these unremarkable superconducting properties, the films
exhibited an extraordinarily high upper critical field. We estimate their
zero-temperature $H_{c2}$ to be more than twice the Pauli limit. Indeed, in 6
nm samples the estimated reduced critical field $H_{c2}/T_c\sim$ 5.6 T/K is
among the highest reported for any elemental superconductor. Although the sheet
resistances of the films were well below the quantum resistance $R_Q=h/4e^2$,
their $H_{c2}$'s approached the theoretical upper limit of a strongly
disordered superconductor for which $k_F\ell\sim1$.
