We just purchased a townhouse and we have the bottom floor. There is another unit above us. There are some ceiling lights in the hallway and kitchen, but nothing in the living room and bedrooms. I would really like to get away from the floor lamps. Is it possible to have lighting added overhead, with anither townhouse above us?

Is this townhouse part of a co-op or home owners association? If yes, you should check because you may not own the rights to the space above your ceiling. The work can be done but would require several access hole be cut into walls and the ceiling.

We are part of a HOA. I'll have to talk to my husband about checking. But, it is possible to add the lighting without having to tamper with anything in the other home?

There is a space between your ceiling and their floor of about 10-12 inches, so yes, there is room to work without desturbing their home. However, as I previously mentioned you need to check with the HOA management to see if this space is yours to occupy or is it considered common space.