expression, i-adjective
has never happened; there is no precedent
Used after the past tense form of a verb to express that something has never occurred or that there is no known instance of it. Often carries a nuance of surprise or emphasis on the lack of precedent.
彼が約束を破ったためしがない。
He has never broken a promise.
こんなに早く雪が降ったためしがない。
It has never snowed this early before.
ためし (例/試し) means 'example' or 'precedent', and がない is the negative form of ある. The phrase literally means 'there is no example' and grammaticalized into an expression meaning 'has never happened'.