Is a minimum size/complexity necessary for an organism to exhibit territoriality?
With some bacteria (e.g.. Bacillus subtilis) when food gets scarce they will start trying to kill their neighbors. (See this arstechnica article) This appears to be a fight to the death between children and parents. That's a kind of territorial behavior, selectively applied only when there are not enough resources to go around. As there is no "recognition" of a specific territory being defended, just wherever the bacteria is currently, this might not meet a strict definition of territorial behavior. But the only thing simpler than bacteria are viruses.

Come to think of it, I bet there are viruses that, once they infect a host cell, will change the cell's membrane or metabolism in a way that reduces its chance of being infected again by a similar virus. Such 'behavior' could be compared to defending a breeding ground. Can't find any examples though.