Eames La Chaise - repairing or sealing chip in fiberglass?  

Bummer. That's a big chip and appears to have been exacerbated, if not caused, by a large void in the original layup. But it's a relatively straightforward repair if you're somewhat handy.
First, fill the void with PC-11 epoxy putty for it's gray-white color. Mix well and allow to fully cure (days). Shape the fill with sandpaper and wipe area thoroughly with acetone. Then, it's a routine gelcoat repair. (it appears to me in your pics to be gelcoat. I've never done one of these, but maybe Vitra can confirm)
Good tutorial here: http://briannystrom.com/?page_id=51
If that looks beyond you, good boatyards and dealers of high-end kayaks do this type of work all the time and can sometimes recommend specialists that travel.
Good luck!

Thank you, this is incredibly helpful. I wouldn't mind trying on a kayak but don't want to risk my favorite piece of furniture! Now to find a local expert...

You're welcome, user.
Decent composite kayaks go for upwards of $3K these days and owners are often at least as obsessively um... detail-oriented as any design aficionado I've met.
Just sayin'!
Meanwhile, you can just take some fine sandpaper to the edges around the chip to minimize the chances of catching clothing or toddlers getting an ouchie. It won't affect the eventual repair.

I brought three Eames shells with a combination of cracks and/or chips in them to a local kayak shop and was very pleased with the results, I second tktoo's advice!