  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 $\sim1\times10^{-3}$ 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 $5\times10^{5}$ 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.
