The layered quasi-one-dimensional molecular superconductor (TMTSF)$_2$PF$_6$ is a very exotic material with a superconducting order parameter whose ground state symmetry has remained ill-defined. Here we present a pulsed NMR Knight shift (K) study of $^{77}$Se measured simultaneously with transport in pressurized (TMTSF)$_2$PF$_6$. The Knight shift is linearly dependent on the electron spin susceptibility $chi_s$, and is therefore a direct measure of the spin polarization in the superconducting state. For a singlet superconductor, the spin contribution to the Knight shift, K$_s$, falls rapidly on cooling through the transition. The present experiments indicate no observable change in K between the metallic and superconducting states, and thus strongly support the hypothesis of triplet p-wave superconductivity in (TMTSF)$_2$PF$_6$.