  We present the first results of a survey of the [CII]158um emission line in
241 luminous infrared galaxies (LIRGs) comprising the Great Observatories
All-sky Survey (GOALS) sample, obtained with the PACS instrument on board
Herschel. The [CII] luminosities of the LIRGs in GOALS range from ~10^7 to
2x10^9 Lsun. We find that LIRGs show a tight correlation of [CII]/FIR with
far-IR flux density ratios, with a strong negative trend spanning from ~10^-2
to 10^-4, as the average temperature of dust increases. We find correlations
between the [CII]/FIR ratio and the strength of the 9.7um silicate absorption
feature as well as with the luminosity surface density of the mid-IR emitting
region (Sigma_MIR), suggesting that warmer, more compact starbursts have
substantially smaller [CII]/FIR ratios. Pure star-forming (SF) LIRGs have a
mean [CII]/FIR ~ 4x10^-3, while galaxies with low 6.2um PAH equivalent widths
(EWs), indicative of the presence of active galactic nuclei (AGN), span the
full range in [CII]/FIR. However, we show that even when only pure SF galaxies
are considered, the [CII]/FIR ratio drops by an order of magnitude, from 10^-2
to 10^-3, with Sigma_MIR and Sigma_IR, implying that the [CII] luminosity is
not a good indicator of the star formation rate (SFR) for most LIRGs, for it
does not scale linearly with the warm dust emission. Moreover, even in LIRGs in
which we detect an AGN in the mid-IR, the majority (2/3) of galaxies show
[CII]/FIR >= 10^-3 typical of high 6.2um PAH EW sources, suggesting that most
AGNs do not contribute significantly to the far-IR emission. We provide an
empirical relation between the [CII]/FIR and the specific SFR (SSFR) for SF
LIRGs. Finally, we present predictions for the starburst size based on the
observed [CII] and far-IR luminosities which should be useful for comparing
with results from future surveys of high-redshift galaxies with ALMA and CCAT.
