Maybe not built in like DTD, closer to XML Schema in its laid-on-top manner, but I would argue that JSON Schema is fairly good, and on its way to becoming an IETF standard: http://json-schema.org/ and https://tools.ietf.org/html/draft-handrews-json-schema-01 (et al)

The lack of obvious namespace management is suboptimal, but so far I thankfully haven't encountered a situation where it was a show-stopper.

IntelliJ and related tools also allow associating a json schema with a YAML file, which I have found infinitely handy

JSON Schema is actually pretty great.