We present HST narrowband near-infrared imaging of Pa and Paβ emission of 48 local luminous infrared galaxies (LIRGs) from the Great Observatories All-Sky LIRG Survey. These data allow us to measure the properties of 810 spatially resolved star-forming regions (59 nuclei and 751 extranuclear clumps) and directly compare their properties to those found in both local and high-redshift star-forming galaxies. We find that in LIRGs the star-forming clumps have radii ranging from ∼90 to 900 pc and star formation rates (SFRs) of ∼1 × 10−3 to 10 M yr−1, with median values for extranuclear clumps of 170 pc and 0.03 M yr−1. The detected star-forming clumps are young, with a median stellar age of 8.7 Myr, and have a median stellar mass of 5 × 105 M . The SFRs span the range of those found in normal local star-forming galaxies to those found in high-redshift star-forming galaxies at z = 1-3. The luminosity function of the LIRG clumps has a flatter slope than found in lower-luminosity, star-forming galaxies, indicating a relative excess of luminous star-forming clumps. In order to predict the possible range of star-forming histories and gas fractions, we compare the star-forming clumps to those measured in the MassiveFIRE high-resolution cosmological simulation. The star-forming clumps in MassiveFIRE cover the same range of SFRs and sizes found in the local LIRGs and have total gas fractions that extend from 10% to 90%. If local LIRGs are similar to these simulated galaxies, we expect that future observations with ALMA will find a large range of gas fractions, and corresponding star formation efficiencies, among the star-forming clumps in LIRGs.