NGC604 is the largest HII-region in M33, second only within the Local Group to 30 Dor, and is important as a laboratory for understanding how massive young stellar clusters interact with the surrounding interstellar medium. Here, we present deep (300ks) X-ray imagery of NGC604 obtained as part of the Chandra ACIS Survey of M33 (ChASeM33), which show highly structured X-ray emission covering ~70% of the full Halpha extent of NGC604. The main bubbles and cavities in NGC604 are filled with hot (kT=0.5keV) X-ray emitting gas and X-ray spectra extracted from these regions indicate that the gas is thermal. For the western part of NGC604 we derive an X-ray gas mass of ~4300M_sol and an unabsorbed (0.35-2.5keV) X-ray luminosity of L_X = 9.3E35 erg/s. These values are onsistent with a stellar mass loss bubble entirely powered by about 200 OB-stars. This result is remarkable because the standard bubble model tends to underpredict the luminosity of X-ray bright bubbles and usually requires additional heating from SNRs. Given a cluster age of ~3Myr it is likely that the massive stars have not yet evolved into SNe. We detect two discrete spots of enhanced and harder X-ray emission, which we consider to be fingerprints from a reverse shock produced by a supersonic wind after it collided with the shell wall. In the eastern part of NGC604 the X-ray gas mass amounts to ~1750M_sol. However, mass loss from young stars cannot account for the unabsorbed X-ray luminosity of L_X = 4.8E35 erg/s. Off-center SNRs could produce the additional luminosity. The bubbles in the east seem to be much older and were most likely formed and powered by stars and SNe in the past.