I've heard a lot of debates between Christians and atheists where the Christian has presented the options for the origin of life on earth as being either (a) intentional design by a creator, or (b) an accident. That is, the word 'accident' is used as if it is the opposite of the word 'design'. I don't think it is, and I think this is a biased way of phrasing the question.
The word 'accident' carries with it loads of negative connotations. People die or are injured in car accidents. Accidents are generally when something goes wrong. The word accident does not just convey the idea of a random event, but it carries the connotation of an unfortunate random event. The word actually implies that there is some right-occurrence which could have happened, but did not happen, and the wrong-occurrence happened instead. The claimed dichotomy between design and accident is false.
The naturalistic atheist does not claim that life evolves by a sequence of unfortunate random events, if anything, the opposite is true. Live evolves because of beneficial, positive random events. Not accidents. There is a better word for this: Serendipity.
Of course the question remains, is life the product of design or serendipity? But that is a better question than is usually presented in these debates.