For example, say you miss a train and therefore meet the love of your life, would this be considered an example of chaos theory?
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"Chaos theory" is sometimes (and quite incorrectly) used as a shorthand for sensitive dependence on initial conditions. That is, in many dynamical systems a slight change in initial state leads to very large differences in long-term trajectories not just for a few special points but for most or all initial states.
Properly speaking, the study of chaos is part of the subject of dynamical systems theory, which is sometimes called chaos theory (but there are many dynamical systems phenomena that are not chaotic).
Real life is full of sensitive dependency on initial conditions (e.g. weather), but also the opposite (e.g. the statistical mechanics behavior of gases). The actual interplay is complex but it is not unreasonable to say that there are enough chaos to describe everyday life as having sensitive dependency. Just note that this does not mean that "anything can happen", just that there is enough nonlinearity (and noise) to make any long-term prediction merely statistical.
No. Life is way more complicated than chaos.
The striking point made by chaos theory is that even seemingly simple systems of a few variables, such as the double pendulum, can be unforeseeable in practice.
While complicated systems exhibiting complicated and hard to predict behavior is not surprising, we can ask whether underneath the apparent confusion there's a hidden order $-$ as when a single, simple square law turned out able to describe the complicated motion of the planets.
But the solar system is also chaotic: even though we understand how the planets and moons move, there's a limit to our prediction power. And our weather is even more of a challenge.
So how does that translate to a human life? Certainly way harder to predict. The same way that turbulence and our atmosphere are probably much more complex than being "simply" chaotic, predicting the future of an individual sentient being, in contact with a complex physical environment containing billions of others, is beyond our capabilities to a degree that's hard to express.
So, is the unpredictability of life an example of chaos theory at work? No, chaos is just one small piece of it.
This small piece has been the subject of some research, though, as can be gleamed from the contents of these books: Chaos Theory in the Social Sciences: Foundations and Applications, edited by L. Douglas Kiel, Euel W. Elliott, Chaos, Catastrophe, and Human Affairs, by Stephen J. Guastello, and Chaos Theory in Psychology and the Life Sciences, edited by Robin Robertson, Allan Combs.