I threw together an iOS app that would do a binary search using this library to interact with the keychain, and determined that the most I could store was an NS(Mutable)String with length 16,777,110. So noticeably less than either the max length of an NSString or the default value of SQLITE_MAX_LENGTH as suggested in other answers.
EDIT: If you're looking to quickly verify this answer, I'd suggest trying to store a String with length 16,777,110 in the keychain, and then trying one with length 16,777,111. If the first one works and the second one doesn't, this answer is correct.
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