Hitomi no Catoblepas(2007)

The story of a guy named Tokio, who's a descendant of a legendary family of youma (demon) fighters. He has the ability to freeze time because of the youma he has in his eye, Catoblepas. One day, he encounters a girl who became a target of a demon. Tokio, with his eye, will try to prevent the girl from becoming another victim of a string of mysterious events that have occured in the town as of late. Little does the girl know that Tokio is her next door neighbour.