The Arches cluster is an extraordinarily compact massive star cluster with a core radius of about 10″ (∼0.4 pc) and consisting of more than 150 O star candidates with initial stellar masses greater than 20 M ⊙ near G0.12-0.02, X-ray observations of the radio Arc near the Galactic center at l ∼ 0°.2, which contains the Arches cluster, have been carried out with the Advanced CCD Imaging Spectrometer (ACIS) on board Chandra X-Ray Observatory. We report the detection of two X-ray sources from the Arches cluster embedded within a bath of diffuse X-ray emission extending beyond the edge of the cluster to at least 90″ × 60″ (3.6 pc × 2.4 pc). The brightest component of the X-ray emission coincides with the core of the cluster and can be fitted with a two-temperature thermal spectrum with a soft and hard component of 0.8 and 6.4 keV, respectively. The core of the cluster coincides with several ionized stellar wind sources that have previously been detected at radio wavelengths, suggesting that the X-ray emission from the core arises from stellar wind sources. The diffuse emission beyond the boundary of the cluster is discussed in the context of combined shocked stellar winds escaping from the cluster. We argue that the expelled gas from young clusters such as the Arches cluster may be responsible for the hot and extended X-ray - emitting gas detected throughout the inner degree of the Galactic center.