Split a JSON file into separate files

I have a large JSON file that is an object of objects, which I would like to split into separate files name after object keys. Is it possible to achieve this using jq or any other off-the-shelf tools?

The original JSON is in the following format

{ "item1": {...}, "item2": {...}, ...}

Given this input I would like to produce files item1.json, item2.json etc.