Is it possible to send an array with the Postman Chrome extension?

You need to suffix your variable name with [] like this:

If that doesn’t work, try not putting indexes in brackets:

my_array[]  value1
my_array[]  value2

Note:

• If you are using the postman packaged app, you can send an array by selecting raw / json (instead of form-data). Also, make sure to set Content-Type as application/json in Headers tab.
  Here is example for raw data {"user_ids": ["123" "233"]}, don’t forget the quotes!

• If you are using the postman REST client you have to use the method I described above because passing data as raw (json) won’t work. There is a bug in the postman REST client (At least I get the bug when I use 0.8.4.6).