M.W.
Yes, they have to give it to you or send it where you want to go. I'd just ask to have my chart copied on your last visit, that's the easiest way.
I had to change doctors (I had both an OB-GYN and MFM doctor) due to a move and both offices just copied my chart for me, and the MFM doctor mailed my most recent ultrasound to the new MFM doctor since it wasn't in my chart yet. You have to sign to have them mail/fax stuff though.