© 2016 AIP Publishing LLC. We have synthesized transparent, conducting, paramagnetic stannate thin films via rare-earth doping of BaSnO3. Gd3+ (4f7) substitution on the Ba2+ site results in optical transparency in the visible regime, low resistivities, and high electron mobilities, along with a significant magnetic moment. Pulsed laser deposition was used to stabilize epitaxial Ba0.96Gd0.04SnO3 thin films on (001) SrTiO3 substrates, and compared with Ba0.96La0.04SnO3 and undoped BaSnO3 thin films. Gd as well as La doping schemes result in electron mobilities at room temperature that exceed those of conventional complex oxides, with values as high as 60 cm2/V·s (n = 2.5 × 1020cm-3) and 30 cm2/V·s (n = 1 × 1020cm-3) for La and Gd doping, respectively. The resistivity shows little temperature dependence across a broad temperature range, indicating that in both types of films the transport is not dominated by phonon scattering. Gd-doped BaSnO3 films have a strong magnetic moment of ∼7 μB/Gd ion. Such an optically transparent conductor with localized magnetic moments may unlock opportunities for multifunctional devices in the design of next-generation displays and photovoltaics.