Deciding between "eponymous" and "titular"

Solution 1:

Titular: Relating to the title.

Eponymous: Giving a name to.

Both are not only appropriate, but often used, as such. Strictly if the collection had been given a name first, and then afterwords the story written for it, then eponymous would be wrong, but that's not the case.

I'd go for eponymous, just because I think it's the phrasing that would come to mind first, and I don't see any reason why I would decide to alter it afterwards. I wouldn't see anything wrong in titular either.

Solution 2:

That which is eponymous gives its name to something else. You could argue that that is what is happening in your example. However, given that the word is typically used in the context of mythical characters who give their names to places or peoples, it seem altogether too overblown to be used in this context. Titular might do, but even that might not be understood. I really think you need to spell it out, and say that your favourite story is the one that gives its name to the whole collection.

Solution 3:

This seems cut-and-dry to me. "Eponymous" gives the name to the title. "Titular" means the title gives its name to something within.

In OP's example, the short story obviously came first. So you'd recommend the eponymous story Burning Chrome.

Solution 4:

I would agree with @jon hanna's definitions, However I think that they suggest that there are times titular is appropriate, but eponymous is not.

Jane Eyre was eponymous because it adopted the character's name, but the Time Traveller's Wife is merely the titular character because she's merely referenced in the title without being specifically named. So I think that eponymous characters are the subset of titular characters that whose name was specifically mentioned in the title.

If this distinction exists, it is likely to disappear over time because people are likely to use eponymous in the looser sense regardless.