We carried out a (CO)-O-18 (J = 1-0) survey for dense molecular cores in the Chamaeleon (Cha) I; II, and III dark clouds with the NANTEN millimeter-wave telescope. The present survey covered similar to 93% of the area where the molecular column density is greater than similar to 4 x 10(21) cm(-2), estimated from preceding (CO)-C-13 (J = 1-0) observations. We identified 23 (CO)-O-18 cores, whose typical mass, radius, peak column density, line width are 22 Mo, 0.22 pc, 9.7 x 1021 cm(-2), and 0.82 km s(-1), respectively. The surface density of classical T Tauri stars abruptly increases for the area whose column density is greater than 10(22) cm-2, suggesting that this value gives a certain threshold value for star formation. The star-formation efficiency varies over a wide range among the three clouds: 13%, 1%, and 0% in Cha I, II, and III, respectively. The (CO)-O-18 cores in Cha I are characterized by (1) a high column density, (2) being almost in virial equilibrium, and (3) a high M-core/M-cloud ratio. The cores in Cha III show the opposite trend, and those in Cha II are in between. Such trends suggest that Cha I is a well-evolved or well gravitationally relaxed cloud-core system, which is probably related to the very high star-formation activity in the cloud.