There are many synonyms for the phrase "by no chance" that convey the same meaning of something being unlikely or impossible. Some examples include "not in a million years," "not a snowball's chance in hell," "no way," "never in a thousand years," and "impossible." All of these expressions emphasize the unlikelihood of a particular event occurring and imply a sense of certainty that it will not happen. Whether used in casual conversation or in more formal settings, these synonyms provide an effective way to convey the same idea of something being out of the realm of possibility.