Not only has there been times in the past when this feature has been asked for but on an equal number of times the suggestion has been either shot down or arguments have developed over the required amount of work to implement it, the number of different languages that would have to be catered for, the number of versions of English and what version of English would be the best to include, etc.
Whilst I usually chat the same way I type anywhere else, with capital letters, correct grammar and spelling, etc, I agree with what others have said here and elsewhere - not enough people care about the presentation of their 'chats' to be bothered with a spell check function.
For this reason and others, I think there are other priorities.
