Hahn/Cock, the latest work to fill the square's empty fourth plinth, is by Katharina Fritsch, the German artist.
The 5-metre tall sculpture was unveiled by city's Mayor Boris Johnson, who, despite his claim that "my critical faculties are exhausted by this wonderful sculpture" had plenty to say on the occasion.
Gleefully feminist, the work pokes amiable fun at the vainglorious statues of men (Nelson, George IV, and generals Havelock and Napier) that surround it in this most imperial of British public spaces, The Guardian reported.
"...It is a symbol of French sporting pride, brought like a chicken to London. We have mounted this French cock at the heart of our imperial square," he said.
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"Humour is always a big thing for me," said Fritsch. "It stops things from becoming too severe. I like English humour. It is so often very dark."
"Art is not made for a few people - it is not an elitist thing."
She said she hoped the work had "many meanings; you can play around with it. It's humorous and also serious".
She noted its context not just among "male persons standing on pedestals" - but amid the present-day cocks of the walk.
The fourth plinth, as it is known, is in the square's north-west corner. Built in 1841, it was designed to hold an equestrian statue, like its twin, in the northeast corner, that depicts George IV. But funds ran out and it remained empty.