The buck stopped here.
YouTube user Jamie-Rae Fifield posted a video showing her 3-year-old French bulldog, Ellie-Mae, chasing a deer around their backyard in Wellington, Nova Scotia. Fifield wrote on YouTube that the two animals had been engaging for about 30 minutes by the time she started filming. Ellie-Mae eventually chased the deer into the woods.
While some YouTube viewers found the encounter adorable, and Fifield wrote that she thought the animals were "playing," others said that it might not have been playful at all and that the deer could have hurt Ellie-Mae.
In general, it's not recommended to let dogs chase after deer (or any wildlife, for that matter). The deer could injure your dog, or your dog might chase it too far and place itself in other kinds of danger.
From the American Society for the Prevention of Cruelty to Animals:
If your dog chases wildlife, he’s putting himself in serious danger. He could chase an animal so far that he becomes disoriented or lost and can’t find his way back to you. He could be shot by a hunter or caught in a trap. Hunters often shoot dogs they see harassing wildlife, such as deer and antelope. Your dog could be wounded or killed by the animal he’s chasing.
H/T Laughing Squid