The main question for me is abiogenesis.
How did the first self-replicating things evolve?
It seems that the kolmogorov complexity of the simplest quines in most languages is relatively high. One would imagine that, in terms of chemistry, the kolmogorov complexity of something that can self-replicate and also evolve with mutations which do not prevent the replication from taking place over generations - ie resilience - is too high to have arisen by mere chance.