The term Christ (English) derives quite directly from the Greek Christos (Χριστός), which is an adjective related to the verb χρίω, which has to do with pouring oil/anointing things with oil. So very literally χριστός when describing things means that it is 'supposed to be smeared on', and when describing persons, means something like 'smeared with oil'.

But, obviously we are talking about the derived use of the word. The Hebrew term Messiah likewise has the meaning of 'person that has been anointed', and the context of the Hebrew Scriptures is that kings, and occasionally other significant figures, are anointed with oil. This, coupled with the expectation of a singular, redemptive figure who would restore Israel's kingdom, i.e. 'the Messiah', led to the term Messiah having its common meaning, something like 'an expected, unique saviour-king'.

It is this meaning that is carried into the religious uses of Christ in, for example, the New Testament. The term designates Jesus as the expected/awaited Messiah-figure, the saviour-king. This meaning derives, as you can see above, from the oil/anointing connection.

It does not mean 'chosen one'. This has no linguistic/historical basis.