Des a Gigabyte GTX 770 fit inside a Zalman Z9 Case?

292mm vs 290 mm seems like "almost"

The Zalman Z9 is 60 x 25 x 60 cm. The GTX 770 is 40 x 25 x 6 cm. You may need a case that's slightly wider.

but you can get a gtx 760 mini, it will fit.

Correction, I found this:
http://us.msi.com/product/vga/N770-2GD5.html268 x 111 x 36mm
http://us.msi.com/product/vga/N770-TF-4GD5-OC.html#specification260x126x38 mm also the 2Gb version is same
http://us.msi.com/product/vga/N770-Lightning.html#/?div=Specification280x129x49.15 mm(w/ GPU Reactor)
Should fit, if your maximum VGA length is 290mm. (also there is OC version of same cards)

Not Gigabyte, but same GPU, and the Lightning looks cool. MSI is one of best quality brands.