Trafalgar Square; a short walk from Sloane Square and South Kensington tube stations. Doesn't sound right, does it? But there was a Trafalgar Square in Chelsea before the other, world-famous, Trafalgar Square had even been built.
What we now know as Chelsea Square was built in 1810. In an area that largely consisted of blocks of flats, it was laid out as houses surrounding a garden, in a bid to encourage wealthier people to the area. The garden became used as a tennis court, and the land was passed on to the Cadogan Estate when the lease expired in 1928.
The Cadogan Estate redeveloped the whole area and demolished the existing houses, replacing them with a mixture of mews houses and Regency style villas, which remain today. The Square was renamed Chelsea Square by 1938 (we wonder how many disappointed tourists had rocked up to the address by then).
By contrast, central London's Trafalgar Square didn't open until 1844, named after the Battle of Trafalgar which took place in 1805. It's not known how Chelsea's Trafalgar Square came by its name, but it was likely named after the same battle, which had taken place only five years prior to the square's construction (Nelson, naturally, was all the rage at that time).
As for why Chelsea gave up the name Trafalgar Square? The Trafalgar Square was probably so well-known by the 1930s, there was no point even trying to compete.
Today, the former Trafalgar Square finds itself in a rather well-to-do part of the city. Chelsea Square is the name of the road that covers three of the four sides of the square. The park area in the centre of the square is officially known as Chelsea Common — ironic perhaps, given that it's off-limits to all expect local residents with keys to those shiny black gates.