The Greek word χριστός, used as a translation of Hebrew משיח "messiah", and meaning something like "anointed" (Liddell and Scott), apparently has a long vowel in the first syllable. The quantity of the vowel would be expected to be the same in the Latinized form Chrīstus.
The use of a long vowel in Chrīstus was brought up in a discussion on the Latin D forum: "long vs short vowel in specific words", but not much evidence was mentioned (only the pronunciation of English "Christ", which could have other explanations). How is the length of the iota in this word known?
I don't know enough about Greek to be able to figure out if the length of the vowel can be inferred from the construction of the word. If this does allow us to rule out a pronunciation with a short vowel, please explain. I know that the related noun χρῖσμα is spelled with a circumflex, which implies that the vowel is long. (The L&S entry mentions the existence of a spelling χρίσμα that it says is misaccented.) Likewise, the verb χρίω has some forms where the vowel is circumflexed, such as χρῖον. But I'm not sure that the presence of a long vowel in these forms guarantees that the vowel in χριστός is also long.
For an example of vowel length changing between related words, Wiktionary says that the verb λύω has a long vowel in Attic in the first-person present form, but that the derivative λύσις has a short vowel.
Data that I know of but that seem inconclusive or irrelevant
Spelling variation in Greek
I know that there seems to have been a variant spelling with eta, χρηστός (and of the adjective, χρηστιανοι). This looks like an iotacistic spelling variant, so I'm not sure that it has any relevance to the issue of vowel length. (Edit: fdb's answer indicates that there were actually semantic reasons for the use of the variant χρηστός. This is interesting, but it makes it seem less likely that χρηστός is useful as a source of information on the pronunciation of the form χριστός. I found a blog post that says a third variant spelled with "ei" is used in some texts from the 3rd to 5th centuries CE, but those also don't seem to me like conclusive evidence of a long vowel in the "anointed" word.)
Romance words that are related to Christus
French has E in the word chrétien (and also in chrême, from χρῖσμα) which is not the normal outcome for Latin ī. However, I think I remember reading that long vowels in closed syllables were often unstable and prone to special shortening changes in Romance languages, so the French forms don't seem to disprove the original existence of a long vowel in the Latin form. French Christ, as well as various other Romance forms, has [i], which is the normal outcome for Latin ī, but that's not conclusive because it's also what would be expected in a learned form (a form borrowed from Latin) regardless of the length of the Latin vowel.
