Which is the correct sentence, if there is a correct one?
I use to be a hitman.
I used to be a hitman.
I've read the second sentence recently in a book, but I was sure it should be I use to be a hitman.
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As reported by the NOAD in a note about the usage of used:
There is sometimes confusion over whether to use the form used to or use to, which has arisen largely because the pronunciation is the same in both cases. Except in negatives and questions, the correct form is used to: we used to go to the movies all the time (not we use to go to the movies). However, in negatives and questions using the auxiliary verb do, the correct form is use to, because the form of the verb required is the infinitive: I didn't use to like mushrooms (not I didn't used to like mushrooms).
About the negative of used to, the NOAD reports the following note:
Traditionally, used to behaves as a modal verb, so that questions and negatives are formed without the auxiliary verb do, as in it used not to be like that and used she to come here? In modern English, this question form is now regarded as very formal or awkwardly old-fashioned, and the use with do is broadly accepted as standard, as in did she use to come here? Negative constructions with do, on the other hand (as in it didn't use to be like that), although common, are informal and are not generally accepted.
See also the Usage section for use in the Oxford Living Dictionaries.
The second is correct.
Your doubts may come from another rule, that following the auxiliary did or didn't, the form use to should be used. For example, if you want to ask someone if they were a hitman, you would say
Didn't you use to be a hitman?
And the answer might be
No I didn't use to be a hitman.
or, as in your example
Yes, I used to be a hitman.
The second one is correct, and this is why:
"used to" means that the person originally had whatever characteristic was being described, but no longer has it. i.e. the person was originally a hitman, but no longer is.
The reason it is in the past tense, is because it is describing something in the past, something that no longer exists, but did in times past.