I saw this headline in the Times of 4 July 2015.
When I first read it, I could not understand the final word on the first word: chicest. I thought for a moment that it must be a typo for choiciest.
In fact, it means 'most chic' (where chic, pronounced /ʃi:k/, means 'fashionable'); it is just the use of the superlative suffix -est added to a fairly common adjective chic. So what's the problem? The -est suffix is fairly productive, so it should not be a problem to add it to an existing adjective.
The problem is this: in English spelling, 'c' followed by 'e' is always pronounced as /s/: cell, ceiling, centre, certain, certificate, ceremony, celestial; receive, deceive, incentive, recent, etc. So when I read the word, I initially imagined that it must be pronounced as /tʃaɪsɪst/.
In most cases, if a word ends with 'c' and then a suffix starting with 'e' is added, then 'k' is inserted: e.g. panicked, picnicked. However, in the case of chic, this is not an option, as chickest would look like something else. As a result, there is no alternative but to have 'c' followed by 'e' in chicest.
The only exceptions to the rule by which 'c' followed by 'e' is pronounced as /s/ that I can think of are: cello, in which the 'c' is pronounced as /tʃ/; and celtic, which starts with /k/ if it refers to a language (but /s/ if it is a football club). So now we seem to have one more: chicest.