What is the cause of chaos (disorder) in a system?

Entropy. The disorder of a system must always increase. The cause of entropy is actually just probability. If you shuffle a deck of cards, it is must more probable that they will end up in a mix up order than ending up in perfect order by suits and numbers. 

If you want to ask about entropy it is best to stick to the technical terms because words like chaos mean something different in mathematics / physics to everyday life, ie a chaotic system (wildly different outcomes for small changes in initial conditions)  is not the same thing as a disordered system (high entropy). And in fact I have never found the terms ordered / disordered to be much help either, since to me, a maximum entropy system descriptively

 looks just as "ordered" as a minimum entropy system, just arranged differently.