The office - which is behind Phase II of the Darwin Centre at the Natural History Museum in central London - will design a new 'learning archive' for the National Maritime Museum in the heart of the Greenwich World Heritage Site in south-east London.
The scheme, which the client hopes will be a 'landmark', is sure to become subject to a massive row with the capital's ever-influential heritage lobby.
And with UNESCO, the agency that runs the processes involved with World Heritage status, beginning to throw its weight around in Britain following a visit to Liverpool, Møller's commission looks troublesome at best.
The project, if it does defy the odds and win a full planning consent, will produce 'dynamic' new facilities for the museum for learning, research and the storage of archival collections.
Despite the prospect of an extremely difficult planning process, museum director Roy Clare said he was convinced that the new building would be open in time to coincide with the 2012 Olympics.
'These are stimulating, creative and dynamic opportunities that will evolve in time for the London Olympics in 2012,' he said.
'C F Møller Architects was chosen because its bid reflected the excitement that we feel about this project and it responded specifically to the opportunities that are presented for opening up and encouraging greater movement of visitors within this spectacular setting in maritime Greenwich,' he added.