Chess I : is actually known as the London production, and was staged for three years at the Prince Edward theater in London. It was preceeded by an album only release of the music from Chess, many of the songs enjoying notable position on the charts in Europe, the UK and the US.
This production was extremely expensive, well up in the millions. It was a multimedia extravaganza, featuring a grid of 64 monitors on each side of the stage, and an addition grid which could be lowered. The stage itself could be tilted and rotated.
Although this version of Chess was very well received, it barely managed to recoup the fortune invested in it. Unfortunately, it was overshadowed by the Phantom of the Opera which opened in 1986. (Tim Rice had actually approached Andrew Lloyd Webber to write Chess, however, Mr. Webber was busy with other projects. The two had previously collaborated on many succesfull ventures together.)
Chess II : was the Broadway release. And was a major rewrite. This was due in part to perestroika which made the United States vs. Russia redundant, and also to attempt to reduce the cost of the production. Florence was rewritten to be American, and was to be played by an American. The stage was completely redesigned. The dances were all but removed, and choreography almost non-existant. The characters were butchered. I could go on, but the best indication of how much the London production was butchered for broadway : Tim Rice all but disowned the project before opening night. Despite this the music was at least on par with "Chess I", and the performances were strong.
The critics tore it a new one. It ran from April to June 1988.