We present an XMM-Newton observation of the long-overlooked radio source G350.1-0.3. The X-ray spectrum of G350.1-0.3 can be fit by a shocked plasma with two components: a high-temperature (1.5 keV) region with a low ionization time scale and enhanced abundances, plus a cooler (0.36 keV) component in ionization equilibrium and with solar abundances. The X-ray spectrum and the presence of non-thermal, polarized, radio emission together demonstrate that G350.1-0.3 is a young, luminous supernova remnant (SNR), for which archival HI and 12-CO data indicate a distance of 4.5 kpc. The diameter of the source then implies an age of only ~900 years. The SNRs distorted appearance, small size and the presence of 12-CO emission along the SNRs eastern edge all indicate that the source is interacting with a complicated distribution of dense ambient material. An unresolved X-ray source, XMMU J172054.5-372652, is detected a few arcminutes west of the brightest SNR emission. The thermal X-ray spectrum and lack of any multi-wavelength counterpart suggest that this source is a neutron star associated with G350.1-0.3, most likely a central compact object, as seen coincident with other young SNRs such as Cassiopeia A.