To get utf8-encoded file as opposed to ascii-encoded in the accepted answer for Python 2 use:

import io, json
with io.open('data.txt', 'w', encoding='utf-8') as f:
  f.write(json.dumps(data, ensure_ascii=False))

The code is simpler in Python 3:

import json
with open('data.txt', 'w') as f:
  json.dump(data, f, ensure_ascii=False)

On Windows, the encoding='utf-8' argument to open is still necessary.

To avoid storing an encoded copy of the data in memory (result of dumps) and to output utf8-encoded bytestrings in both Python 2 and 3, use:

import json, codecs
with open('data.txt', 'wb') as f:
    json.dump(data, codecs.getwriter('utf-8')(f), ensure_ascii=False)

The codecs.getwriter call is redundant in Python 3 but required for Python 2

Readability and size:

The use of ensure_ascii=False gives better readability and smaller size:

>>> json.dumps({'price': '€10'})
'{"price": "\\u20ac10"}'
>>> json.dumps({'price': '€10'}, ensure_ascii=False)
'{"price": "€10"}'

>>> len(json.dumps({'абвгд': 1}))
37
>>> len(json.dumps({'абвгд': 1}, ensure_ascii=False).encode('utf8'))
17

Further improve readability by adding flags indent=4, sort_keys=True (as suggested by dinos66) to arguments of dump or dumps. This way you'll get a nicely indented sorted structure in the json file at the cost of a slightly larger file size.