The combination of the two characters means "dangerous situation" in both Chinese and Japanese, but the kanji 機 in Japanese means "opportunity".

But let's not take anything away from Western languages.

The etymology of our word "crisis" is not a negative term at all but derives from the Greek verb κρίνω, krino, or "separate, distinguish, choose". This writes Maddalena de Bernardi in a comment. In Chinese, crisis is written in the same way as in Japanese, but the two ideograms have a slightly different meaning and are closer to Western etymology. 

危機 is pronounced wēijī, 危 means "danger" and 機 "crucial point, initial moment" or rather when something begins or changes, a crossroads.

This is what a Chinese professor writes in a very long article. The three languages examined are not so distant, in all of them there is the concept of choice, of the crossroads which has one aspect of danger and another of opportunity.