From a short story:
I showed it to him. He seized the pages with immediate pleasure, as if greeting an old friend. "Would you like to work through it? I have yearned for the chance to speak to a true geometer."
Would it be grammatical to change the article:
I showed it to him. He seized the pages with immediate pleasure, as if greeting an old friend. "Would you like to work through it? I have yearned for a chance to speak to a true geometer."
It seems to me that the second option is better. The hero yearned for any chance to speak to a true geometer, after all, not for this particular chance. But maybe I'm wrong.