The PLA (Programmable Logic Array) is a very common chip to fail in a C64. A typical scenario with a faulty PLA: a C64 has been sitting in the attic for years, and is returned back to use. It seems to work at first, but then, after a few hours of use, it suddenly malfunctions. If this happens, the PLA should be prime suspect. One possible explanation for this is that the chip suffers from inadequate passivation (presumably more so than the other chips in a C64), making it vulnerable to moisture and oxidation. So it's likely the damage has already been done during the storage period, and after the chip heats up during the first hours of use, the problem simply manifests itself. After this stage the symptoms are usually permanent and display upon every boot.
Some common symptoms include a simple black screen and flashing/rainbow colored startup screen characters. A failed PLA will sometimes get very hot. If the chip becomes hot in a matter of seconds after switching on, it's likely dead. Generally if you get an incorrect startup with flashy/colorful/animating graphics, the PLA and VIC-II are prime suspects.
The older the PLA model, the more failure prone it seems to be. Sometimes they fail spontaneously without any storage period involved. The older PLAs also tend to run hotter than the newer ones. The C64c models feature a new type of PLA chip that is known to rarely fail.
Although it's hard to prove any of the following tips have any real effect on preventing a PLA failure, they may at least help prolong the life of a PLA chip:
CAUTION: When swapping PLA chips, make sure you don't mistake a SID for a PLA. They are the same size, and the chip locations vary depending on board revision. You will likely kill either chip if you put it in the wrong socket and switch on the C64.