We have completed a ¹³CO (J=1-0) survey for molecular clouds toward the Chamaeleon-Musca Dark Cloud Complex, covering an ~16° × 17° area with the NANTEN millimeter-wave telescope. The major result is a discovery of 25 small dense clouds widely distributed over ~11° × 13° ( ~28 × 33 pc at ~140 pc), in addition to the four previously known large dark clouds. The small clouds show a good spatial correlation with the 33 isolated X-ray-emitting T Tauri stars (TTSs), and most ( ~70%) of the 33 TTSs located within 4 pc of the small clouds' boundaries are likely formed in the small clouds. It is argued that the average density, 10³ cm⁻³, and mass, ~20 M, of the small clouds are large enough to form stars in them. The apparent lack of the associated molecular gas for the remaining TTSs is plausibly explained as a result of cloud dissipation due to the outflow activity of the X-ray TTSs. Based on the present findings, we conclude that the X-ray TTSs were formed in the small dense clouds and that it is not necessary to invoke a runaway TTS hypothesis.