Chinless wonder is a derogatory term for an upper-class (or sometimes middle-class) person, often a Brit

British people

The British are citizens of the United Kingdom, of the Isle of Man, any of the Channel Islands, or of any of the British overseas territories, and their descendants...

, frequently one who gained his position via nepotism or other social connections, not through his own competence. The term is derived from the characteristic recessive chin of some rich people, which is thought to be caused by inbreeding, traditionally common among the upper-classes, although a person need not be literally 'chinless' to be described as a chinless wonder. The 'wonder' part of the term is often replaced with an offensive word to greaten the insult.

References:

1-Urban Dictionary entry for Chinless wonder.

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