In Python:
import json
with open('file.json') as infile:
o = json.load(infile)
chunkSize = 1000
for i in xrange(0, len(o), chunkSize):
with open('file_' + str(i//chunkSize) + '.json', 'w') as outfile:
json.dump(o[i:i+chunkSize], outfile)
