The SETI project - the Search for Extra Terrestrial Intelligence - has been underway for years now, trying to attract alien attention to Earth by broadcasting radio signals and monitoring responses. For some scientists, however, contact has already been received, and there's measurable proof.
In 1977, the 'Big Ear' radio telescope in Ohio received a transmission that seemed to come from somewhere towards the constellation of Sagittarius and ticked all of the boxes for what an alien transmission should look like. The broadcast lasted for 72 full seconds, and although we have made multiple attempts to respond, has never been repeated. Despite this, no satisfactory scientific explanation for the broadcast has ever been found, and a broadcast from an alien civilization remains the most likely cause.