Hi there,
Chaining (in this context) is mostly for not having to cache selectors, especially handy with binding event handlers.
And of course for code sexiness points and readability...
One jQuery selector at the start and than you can just chain the whole thing without having to store the jQuery object in some var.
The situation becomes different when you have binding logic in separate places, in that case you can probably think of repositioning your logic so that all event handlers could be chained but that's beside the point...
Than it is faster to cache the jQuery object so you don't have DOM access every time.
Not caching the jQuery object also eliminates the chance of variables leaking into global namespace and all, but this of course is only relevant when you have one chain which you only use once.
Just to be on the safe side here I'm not saying you shouldn't cache jQuery objects ;)
But I'll be very surprised if there's any noticeable performance difference between the two approaches.
The biggest performance gain in this situation would be not having to download the bytes you need to write $var = $(someselector)
Which also is marginal.
Superficial.