Considering order and chaos gives us a useful glimpse into the nature of reality. The world seems to flow with an appearance of both order and chaos. By 'chaos' I mean the opposite of orderliness, which we can describe as randomness, where things happen by chance. For example, a tree grows according to the orderly 'pattern' stored in the seed, but chaos applies in the formation of the tree, giving rise to its uniqueness. So no two trees are the same. They follow a pattern (order) but there is chance (chaos) in where and how the branches grow.
Let's consider emptying a pencil case onto a table. If we tip up the case and let the stationery fall out it lands on the table in a chaotic fashion, with pens, pencils, rulers, erasers and so on scattered randomly. So there appears a scene of orderly objects scattered chaotically. It appears chaotic but there is an argument that the chaotic scattering is actually orderly. That is, the objects fall according to gravity and a complex array of forces applying to each object as they fall. These forces are the orderly forces of nature. The appearance of randomness is then not so random, but determined by natural forces. Similarly, the branches of a tree grow according to its orderly plan and the forces of nature, including gravity, the wind, the sun and other environmental factors.
It can be considered that Chaos is merely a play of order, where order creates the appearance of chaos, similar to how numbers are 'randomly' generated in a computer game. Random number generation in computer games often uses a 'seed' number, which can be taken from the computer's clock time and fed it into a complex algorithm to produce apparently random numbers that can trigger events in the game. So it's not really random. Other things can be used for the 'seed' number, such as the fluctuating electrical power supply, and that brings a more chaotic element to the randomness. But it could be argued that the power supply fluctuates in an orderly manner, according to nature's laws.
So is Chaos real? There is a scientific view that quantum physics is completely random, that there are random fluctuations in the quantum realm that are not orderly and give rise to randomness in the world. Or maybe it is just another appearance of randomness that will be found to have an orderly source.
From the Non Dual perspective there is not this play of order and chaos. There is only an appearance of opposites in separation, just as there is only an appearance of 'order and chaos'. The Reality is that there is only One, an Infinite One without division, form or limitation. In itself the One can be considered as complete order, as there is no confusion or randomness in simply being. It is an Order beyond the sense of 'order and chaos'.