The cluster NGC 3603 hosts some of the most massive stars in the Galaxy. With a modest 50 ks exposure with the Chandra High Energy Grating Spectrometer, we have resolved emission lines in spectra of several of the brightest cluster members which are of WNh and O spectral types. This observation provides our first definitive high-resolution spectra of such stars in this nearby starburst region. The stars studied have broadened X-ray emission lines, some with blue-shifted centroids, and are characteristic of massive stellar winds with terminal velocities around 2000--3000 km/s. X-ray luminosities and plasma temperatures are very high for both the WNh and O stars studied. We conclude that their X-rays are likely the result of colliding winds.