The Kepler mission showed us that planets with sizes between that of Earth and Neptune appear to be the most common type in our Galaxy. These super-Earths continue to be of great interest for exoplanet formation, evolution, and composition studies. However, the number of super-Earths with well-constrained mass and radius measurements remains small (40 planets with $sigma_{rm{mass}}<$ 25%), due in part to the faintness of their host stars causing ground-based mass measurements to be challenging. Recently, three transiting super-Earth planets were detected by the K2 mission around the nearby star GJ 9827/HIP 115752, at only 30 pc away. The radii of the planets span the radius gap detected by Fulton et al. (2017), and all orbit within ~6.5 days, easing follow-up observations. Here we report radial velocity (RV) observations of GJ 9827, taken between 2010 and 2016 with the Planet Finder Spectrograph on the Magellan II Telescope. We employ two different RV analysis packages, SYSTEMIC and RadVel, to derive masses and thus densities of the GJ 9827 planets. We also test a Gaussian Process regression analysis, but find the correlated stellar noise is not well constrained by the PFS data, and that the GP tends to over fit the RV semi-amplitudes resulting in a lower K value. Our RV observations are not able to place strong mass constraints on the two outer planets (c & d) but do indicate that planet b, at 1.64 R$_{oplus}$ and ~8 M$_{oplus}$, is one of the most massive (and dense) super-Earth planets detected to date.