Most stars form as members of large associations within dense, very cold (10-100 K) molecular clouds. The nearby giant molecular cloud in Orion hosts several thousand stars of ages less than a few million years, many of which are located in or around the famous Orion Nebula, a prominent gas structure illuminated and ionized by a small group of massive stars (the Trapezium). We present X-ray observations obtained with the X-ray Multi-Mirror satellite XMM-Newton revealing that a hot plasma with a temperature of 1.7-2.1 million K pervades the southwest extension of the nebula. The plasma, originating in the strong stellar winds from the Trapezium, flows into the adjacent interstellar medium. This X-ray outflow phenomenon must be widespread throughout our Galaxy.