Would it be possible to regionally label the group and make it open to the community but ask your employer to use a room in the facility to host the mtg - just like a weight watchers group might. Just as an FYI, Chris has an important note about starting with HR. And from HR's perspective you'll want to say clear of using employer webboards etc. for the group.
If you open it up to non-ee's and just request to use a mtg room - probably during non-work time or if lunch is accepted as personal time... Support is a wonderful thing.