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The pronunciation of the initial c in the English words Celt and Celtic in their various meanings can be realised either as /k/ or /s/ (that is, either hard or soft). Both can be justified philologically and both are "correct" in English prescriptive usage.
Although the word originated in an early Continental Celtic language, it came to English via Greek (Keltoi), where it is spelled with a kappa; thus /k/ is the original pronunciation. This was borrowed into Latin (Celtae), where it was likewise pronounced with /k/. However in the transition from Classical Latin to Vulgar Latin and early Romance, this sound shifted to /t?/, a process known as palatalisation, and in French further to /s/. Under French influence, the practice c representing /s/, when used before the vowels "i" and "e," in words of Latin origin became established in English, as for example celestial, cilia, and Cicero. Thus /s/ is the inherited pronunciation in English for these words.
Until the mid-20th century, Celtic was usually pronounced with /s/ in English except by academics, but the pronunciation with /k/ has been gaining ground recently. Following the usage of philologists, /k/ is now almost invariably used with reference to Celtic culture even in non-academic contexts.
However, the /s/ pronunciation remains the most recognised form when it occurs in the names of sports teams, most notably Celtic Football Club and the Boston Celtics basketball team.
Source: http://en.wikipedia.org/wiki/Names_of_the_Celts
