Bruichladdich is one of the fifty most unpronounceable names in Scotland says the Scottish Miscellany.
The full Gaelic name is Brudhach a Chladdaich, two descriptive geographical words. Brudhach is pronounced 'brew-ahhk' (with the 'hach' heavily aspirated), while in the softer Islay Gaelic accent, Chladdich, sounds like 'klah-dee' or 'klah-deehk'.
Put together we get 'brew-ahhk-ah-klah-dee-hk'. Over time, the end of the first word, and the beginning of the second were elided to become 'brew-ah-kladdie'. This was ultimately Anglicised in the nineteenth century to ‘broo-kladdie’.
West Coast Gaelic speakers still pronounce it as 'brew-ah-kladdie'.