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.