We present new CO(2-1) observations of a representative sample of 24 local (z<0.02) luminous infrared galaxies (LIRGs) at high spatial resolution (<100 pc) from the Atacama Large Millimeter/submillimeter Array (ALMA). Our LIRGs lie above the Main-Sequence (MS), with typical stellar masses in the range 10 10 -10 11 M and SFR∼30 M yr −1 . We derive the effective radii of the CO(2-1) and the 1.3 mm continuum emissions using the curve-of-growth method. LIRGs show an extremely compact cold molecular gas distribution (median R CO ∼0.7 kpc), which is a factor 2 smaller than the ionized gas (median R Hα ∼1.4 kpc), and 3.5 times smaller than the stellar size (median R star ∼2.4 kpc). The molecular size of LIRGs is similar to that of early-type galaxies (ETGs; R CO ∼1 kpc) and about a factor of 6 more compact than local Spirals of similar stellar mass. Only the CO emission in low-z ULIRGs is more compact than these local LIRGs by a factor of 2. Compared to high-z (1