The customer is always right
The trading policy that states a company's keenness to be seen to put the customer first.
Several retail concern used this as a slogan from the early 20th century onward. In the USA it is particularly associated with Marshall Field's department store, Chicago (established in the late 19th century). The store is an icon of the city, although it is set to lose its name in 2006 when, following a takeover, it becomes renamed as Macy's. In the UK, Harry Gordon Selfridge (1857-1947) the founder of London's Selfridges store (opened in 1909), is credited with championing its use. The Wisconsin born Selfridge worked for Field from 1879 to 1901. Both men were dynamic and creative businessmen and it's highly likely that one of them coined the phrase, although we don't know which.
Of course, these entrepreneurs didn't intend to be taken literally. What they were attempting to do was to make the customer feel special by inculcating into their staff the disposition to behave as if the customer was right, even when they weren't.
The trading policy and the phrase were well-known by the early 20th century. From the Kansas City Star, January 1911 we have a piece about a local country store that was modelled on Field's/Selfridges:
[George E.] "Scott has done in the country what Marshall Field did in Chicago, Wannamaker did in New York and Selfridge in London. In his store he follows the Field rule and assumes that the customer is always right."
Whether the phrase was coined by Field or Selfridge it is fair to call it American. What we can't do is credit them with the idea behind it. In 1908 César Ritz (1850-1918), the celebrated French hotelier is credited with saying 'Le client n'a jamais tort' - 'The customer is never wrong'. That's not the phrase that people now remember, but it can hardly be said to be any different in meaning to 'the customer is always right'.
See other phrases that were coined in the USA.