Observations of helium and hydrogen emission lines from metal-poor extragalactic H II regions, combined with estimates of metallicity, provide an independent method for determining the primordial helium abundance, Yp. Traditionally, the emission lines employed are in the visible wavelength range, and the number of suitable lines is limited. Furthermore, when using these lines, large systematic uncertainties in helium abundance determinations arise due to the degeneracy of physical parameters, such as temperature and density. Recently, Izotov, Thuan, & Guseva (2014) have pioneered adding the He I λ10830 infrared emission line in helium abundance determinations. The strong electron density dependence of He I λ10830 makes it ideal for better constraining density, potentially breaking the degeneracy with temperature. We revisit our analysis of the dataset published by Izotov, Thuan, & Stasi'nska (2007) and incorporate the newly available observations of He I λ10830 by scaling them using the observed-to-theoretical Paschen-gamma ratio. The solutions are better constrained, in particular for electron density, temperature, and the neutral hydrogen fraction, improving the model fit to data, with the result that more spectra now pass screening for quality and reliability, in addition to a standard 95% confidence level cut. Furthermore, the addition of He I λ10830 decreases the uncertainty on the helium abundance for all galaxies, with reductions in the uncertainty ranging from 10–80%. Overall, we find a reduction in the uncertainty on Yp by over 50%. From a regression to zero metallicity, we determine Yp = 0.2449 ± 0.0040, consistent with the BBN result, Yp = 0.2470 ± 0.0002, based on the Planck determination of the baryon density. The dramatic improvement in the uncertainty from incorporating He I λ10830 strongly supports the case for simultaneous (thus not requiring scaling) observations of visible and infrared helium emission line spectra.