We present Keck NIRSPEC and Keck NIRES spectroscopy of sixteen metal-poor galaxies that have pre-existing optical observations. The near-infrared (NIR) spectroscopy specifically targets the HeI{lambda}10830{AA} emission line, due to its sensitivity to the physical conditions of the gas in HII regions. We use these NIR observations, combined with optical spectroscopy, to determine the helium abundance of sixteen galaxies across a metallicity range 12+log_10_(O/H)=7.13-8.00. This data set is combined with two other samples where metallicity and helium abundance measurements can be secured: star-forming galaxies selected from the Sloan Digital Sky Survey spectroscopic database, and existing low-metallicity systems in the literature. We calculate a linear fit to these measurements, accounting for intrinsic scatter, and report a new determination of the primordial helium number abundance, y_P_=0.0805_-0.0017_^+0.0017^, which corresponds to a primordial helium mass fraction Y_P_=0.2436_-0.0040_^+0.0039^. Using our determination of the primordial helium abundance in combination with the latest primordial deuterium measurement, (D/H)_P_x10^5^=2.527+/-0.030, we place a bound on the baryon density {Omega}_b_h^2^=0.0215_-0.0005_^+0.0005^ and the effective number of neutrino species N_eff_=2.85_-0.25_^+0.28^. These values are in 1.3{sigma} agreement with those deduced from the Planck satellite observations of the temperature fluctuations imprinted on the cosmic microwave background.