The likelihood of life happening as we see it by chance and not design is unlikely.
First, the opposite of design is NOT chance.
The opposite of design is undesigned. For example, the formation of a star happens via processes that are understood, that we see happening today, and that do not involve intelligent intervention. This is a process that is not designed, but it is also not 'by chance'. The simple action of gravity is enough to make it happen.
Second, you *claim* it is unlikely to happen without design, but since we don't know the process for it to happen, we don't know that it would require intelligent intervention. Furthermore, there are no likely intelligent agents that have been verified to be around at that time, so the likelihood of an intelligent intervention is very, very low.
Third, the original life was NOT life 'as we see it' today. For one thing, it was ALL single celled. It was also anaerobic: oxygen was actually poison to early life. But since there was very little oxygen in the atmosphere at that time, this was not a problem for the life that existed then. It wasn't for another 2 billion years or so that more complex cells developed that produced oxygen in abundance (causing a massive die off of previous forms of life). Only after that did plants, animals, and eventually humans develop.