We present IRAM PdBI observations of the CO(3-2) and CO(5-4) line transitions from a Ly-alpha blob at z~2.7 in order to investigate the gas kinematics, determine the location of the dominant energy source, and study the physical conditions of the molecular gas. CO line and dust continuum emission are detected at the location of a strong MIPS source that is offset by ~1.5 from the Ly-alpha peak. Neither of these emission components is resolved with the 1.7 beam, showing that the gas and dust are confined to within ~7kpc from this galaxy. No millimeter source is found at the location of the Ly-alpha peak, ruling out a central compact source of star formation as the power source for the Ly-alpha emission. Combined with a spatially-resolved spectrum of Ly-alpha and HeII, we constrain the kinematics of the extended gas using the CO emission as a tracer of the systemic redshift. Near the MIPS source, the Ly-alpha profile is symmetric and its line center agrees with that of CO line, implying that there are no significant bulk flows and that the photo-ionization from the MIPS source might be the dominant source of the Ly-alpha emission. In the region near the Ly-alpha peak, the gas is slowly receding (~100km/s) with respect to the MIPS source, thus making the hyper-/superwind hypothesis unlikely. We find a sub-thermal line ratio between two CO transitions, I_CO(5-4)/I_CO(3-2)=0.97+/-0.21. This line ratio is lower than the average values found in high-z SMGs and QSOs, but consistent with the value found in the Galactic center, suggesting that there is a large reservoir of low-density molecular gas that is spread over the MIPS source and its vicinity.
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