We present $HST$ narrow-band near-infrared imaging of Pa$alpha$ and Pa$beta$ emission of 48 local Luminous Infrared Galaxies (LIRGs) from the Great Observatories All-Sky LIRG Survey (GOALS). These data allow us to measure the properties of 810 spatially resolved star-forming regions (59 nuclei and 751 extra-nuclear 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 $sim90-900$ pc and star formation rates (SFRs) of $sim1times10^{-3}$ to 10 M$_odot$yr$^{-1}$, with median values for extra-nuclear clumps of 170 pc and 0.03 M$_odot$yr$^{-1}$. The detected star-forming clumps are young, with a median stellar age of $8.7$ Myrs, and a median stellar mass of $5times10^{5}$ M$_odot$. The SFRs span the range of those found in normal local star-forming galaxies to those found in high-redshift star-forming galaxies at $rm{z}=1-3$. 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 future observations with ALMA will find a large range of gas fractions, and corresponding star formation efficiencies, among the star-forming clumps in LIRGs.
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