My pup has also started doing this! We live in the country so I am not afraid she will get ran over but she will chase after deer! Yesterday I was chasing after her, chasing after a deer and she went all the way to the beginning of the woods!
I got really scared because if I was not paying attention she could have went in and gotten lost
She will also get the deer poop (gross I know) in her mouth and want me to chase her around the yard. I started today putting her on her leash every time she went out side. The risk is not worth the extra 10 seconds it takes to put it on and take it off.