|Some of my grass is turning brown, yellowish, hay-like, and it seems to be spreading, like something is|
|Without inspecting the affected grass and the soil, it's difficult to diagnose the problem. However, if it is isolated along the chainlink fence, is it possible that herbicides were sprayed on the affected lawn? This is about the only thing that would produce the pattern of dead grass you describe. Maybe a discussion with your neighbor will shed a little more light on the subject. Be sure to check your sprinklers, too. Sometimes water doesn't reach every place in the landscape. To repair, rake out the dead grass and reseed the area. New grass should sprout in 7-10 days.
Best wishes with your lawn!