Any statement about causation or origin which uses the word chance is worthless, philosophically. The academic credentials or prestige of the person making such a statement is unimportant, the statement is still worthless.
Take for example the basic belief held by most astronomers and atheists prior to Vesto Slipher's expanding universe discovery in 1913, "the Universe simply exploded into being, by chance, at the big bang, and thus there's no need for any God." Or ponder the words of the Nobel scientist Jacques Monod in his book Chance and Necessity, "...chance alone is at the source of every innovation, of all creation in the biosphere. Pure chance, absolutely free, but blind at the very root of the stupendous edifice of evolution..." (page 112)
Let me alert you to the fact that, though we tend to use the word chance loosely, chance is not a substance or entity that can cause anything. Chance is not an entity with causal power. Chance is a non-entity, technically chance is no thing=nothing. Chance is a word we use when we mean to say "not planned by anyone".
If my reasoning is correct, Monod is saying, in effect, that a non-entity, a veritable nothing is at the root of evolution. Similarly concerning the big-bang explosion into being of the universe by chance the dubious mechanism is a non-entity, a veritable nothing.
Any theory which is designed to show how a thing has come into being must wield explanatory power and explanatory scope. By explanatory power I mean it must adequately explain the crucial aspects of the phenomenon under study, and by explanatory scope I mean it must provide clarity on not just a few but on most of the crucial aspects of the phenomenon under study. Chance has neither explanatory scope nor power concerning anything because it is not a causal entity.
So then, when scientists say "by chance" they are not providing a mechanism to explain anything, it is simply wishful thinking and must be unmasked as such. Ponder the following additional scientific statements.
Specialist in the Philosophy of Science Dr Stephen Myer in his fascinating recent book Signature in the Cell: DNA and the Evidence for Intelligent Design evaluates scientific theories that argue for a non-design origin of life and of biological information.
He says about proponents of such theories: "They often say things like 'Sure, the origin of life is overwhelmingly improbable, but as long as there is at least some chance of life arising by chance, then we shouldn't reject the possibility that it did.'" (page 220). Later he writes "To say that 'given infinite time, life might have arisen by chance' was, in essence, a tautology. Given infinite time, anything might happen..." (page 224).
Dr Meyer concedes too much in this latter quotation. The 'infinite time...life might have arisen by chance' quotation is not so much tautologous as it is sheer wishful thinking and incapable of scientific demonstration. Worse, it compounds the dubious appeal to the non-entity 'chance' by appealing to another non-causal [and possible non-] entity 'time'.
Time cannot at all explain the origin of anything because time like chance is not causative. Time is what we call the gap between non-simultaneous events. So even if infinite time is a conceptual reality, by itself or combined with chance, no entity's origin can be satisfyingly explained.
We all need to rethink and re-read all claims made for 'chance' in the realm of origins.