A most difficult one, indeed!

[Clearing her throat, Alice begins to recite it eloquently.]

"John gave his brother James a box:
About it there were many locks.

James woke and said it gave him pain;
So gave it back to John again.

The box was not with lid supplied,
Yet caused two lids to open wide;

And all these locks had never a key-
What kind of box, then, could it be?"