  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 10830A 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 (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, which
corresponds to a primordial helium mass fraction Y_P = 0.2436+/-0.0040. Using
our determination of the primordial helium abundance in combination with the
latest primordial deuterium measurement, (D/H)_P x 10^5 =2.527+/-0.030, we
place a bound on the baryon density Omega_bh^2 = 0.0215+/-0.0005 and the
effective number of neutrino species Neff = 2.85+/-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.
