From Greek Χριστος (Christos) meaning "anointed", derived from χριω (chrio) meaning "to anoint". This was a name applied to Jesus by early Greek-speaking Christians. It is a translation of the Hebrew word מָשִׁיחַ (mashiyach), commonly spelled in English messiah, which also means "anointed".
This is a modern Greek name as well, though it is commonly spelled Χρηστος. The two spellings are pronounced identically in modern Greek.