OK so I made a 2 minute search on the net and found out that the term fair chase stems from Theodore Roosevelt andfriends, in the Boone and Crocket club, at the turn of thelast century. And by the guys that defined it, fences is clearly not considered Fair chase since fenced game is not free ranging. But, just as clearly, it can never be fair chase with small game or game, not native to America.
But the real question was perhaps if it ca be considered ethical and sportsmanlike which I find it possible to be. I do not have a problem with deer farms either.In fact Ilike them,since they bring more people into eating venison and hence increase peoples open mindness to hunting. Anyway heres the link:

http://www.boone-crockett.org/huntingEthics/ethics_fairchase.asp?area=huntingEthics