Chance would be...

[fredpuli47]

" Chance would be a fine thing!" is commonly said without 'the' or 'a' at the beginning, which gives the expression an ancient air, as though, in the manner of old writers, Chance is personified.

.How old is it?

[Quizmonster]

'The' or 'a' is normally implicit, if not actually stated, when the phrase is used.
A. Have you bedded the new barmaid?
B. Chance would be a fine thing!
Surely B is saying that he would very much appreciate the opportunity, but - perhaps because he is a drunk, is getting on in years, is ugly or whatever else might preclude her looking kindly upon him - he realises that there isn't much likelihood that she ever will.
The OED isn't much help on this one. Partridge suggests the phrase has virtually become a proverb. The earliest example he could find is in the play, Hindle Wakes, dated 1912, though he also suspects it nay date back to Restoration times.