Germany: Angela Merkel 'loses key state election'
The results gave the Greens 24.2% and their Social Democrat allies 23.1%, with Mrs Merkel's party on 39% and its Free Democrat (FDP) allies on 5.3%.
Nuclear power, following the accident in Japan, was a key issue.
The vote in the wealthy south-western state was seen as a referendum on Mrs Merkel's rule.
The region, around Stuttgart, has a population of some 11 million and has been ruled by the Christian Democrats since 1953.
If the Greens do go into coalition with the Social Democrats, it will be the first time they have held power in a state.
Green party spokesman Franz Untersteller said: "It's a dream come true... we could never have dreamed of a result like this a few days ago."
Christian Democrat state governor Stefan Mappus, an advocate of nuclear energy, said: "Voters were touched by the terrible events in Japan; those images still haunt people today"; Kazinform cites BBC News.
See www.bbc.co.uk for full version.