We present the first results of a survey of the CII157.7 mu m emission line in 241 luminous infrared galaxies (LIRGs) comprising the Great Observatories All-sky LIRG Survey (GOALS) sample, obtained with the PACS instrument on board the Herschel Space Observatory. The CII luminosities, L sub(CII), of the LIRGs in GOALS range from ~10 super(7) to 2 x 10 super(9) L sub(middot in circle). We find that LIRGs show a tight correlation of CII/FIR with far-IR (FIR) flux density ratios, with a strong negative trend spanning from ~10 super(-2) to 10 super(-4), as the average temperature of dust increases. We find correlations between the CII/FIR ratio and the strength of the 9.7 mu m silicate absorption feature as well as with the luminosity surface density of the mid-IR emitting region (summationoperator sub(MIR)), suggesting that warmer, more compact starbursts have substantially smaller CII/FIR ratios. Pure star-forming LIRGs have a mean CII/FIR ~ 4 x 10 super(-3), while galaxies with low polycyclic aromatic hydrocarbon (PAH) equivalent widths (EWs), indicative of the presence of active galactic nuclei (AGNs), span the full range in CII/FIR. However, we show that even when only pure star-forming galaxies are considered, the CII/FIR ratio still drops by an order of magnitude, from 10 super(-2) to 10 super(-3), with summationoperator sub(MIR) and summationoperator sub(IR), implying that the CII157.7 mu m luminosity is not a good indicator of the star formation rate (SFR) for most local LIRGs, for it does not scale linearly with the warm dust emission most likely associated to the youngest stars. Moreover, even in LIRGs in which we detect an AGN in the mid-IR, the majority (2/3) of galaxies show CII/FIR > or =, slanted 10 super(-3) typical of high 6.2 mu m PAH EW sources, suggesting that most AGNs do not contribute significantly to the FIR emission. We provide an empirical relation between the CII/FIR and the specific SFR for star-forming LIRGs. Finally, we present predictions for the starburst size based on the observed CII and FIR luminosities which should be useful for comparing with results from future surveys of high-redshift galaxies with ALMA and CCAT.