On the night of the 20th of February 2008 there was a total eclipse of the moon visible from Mexico City, with a total duration from 19:42 hrs to 23:09 hrs. At the Instituto de Astronomía, UNAM, we took this opportunity to organise a massive astronomical party on the central plaza of the city, the Zocalo. Over a period of about 6 hrs. we set up a huge astro-party, with free use of over 100 telescopes, where we estimate over 40,000 persons looked through an astronomical telescope at the moon and Saturn, most for the first time in their lives. Numerous stands including a children's games, an Astronomy conference room, and the free distribution of Astronomical material were organised. Here we describe some of the issues associated with the planning and implementation of the event. Coordination issues were complex, involving interaction with divers and numerous authorities, city, national, police, traffic, medical assistance in readiness, aide from other universities, and amateur astronomical societies, which supplied most of the telescopes. An extensive publicity campaign was launched with several weeks of anticipation, and although we had no way of estimating the public response, we were ready with over 800 volunteers at the Zócalo on the 20th of February. The public response was massive and overwhelmingly positive, thousands swarmed the square in a completely peaceful and well organised interaction between Astronomy and society at large, over many complementary levels