On this server I always thought half giants had to start off as partially chaotic as well. Of course giant species range across the whole spectrum of extremes, LE for Fire and Frost, CE for Hill and various oafish types, NE for Forrest ones, Goodly titans and cloud giants, CN Stone ones, and countless other variations of giantkin. We'd have to specify exactly what type of Giant we're talking about here...
I always wished there were a byline where you could be lawful if you took the feat for /5 Natural DR for either cold or fire, signifying which type of parentage you held. Chaotic Rock types could take improved Fortitude, Goodly cloud halfbreeds DR /5 electric... etc, and must be chaotic without any feats for the now standard, Hill Giant descendant. It'd make the half-giant race mirror Grannoch's faith and lineage more appropriately, letting the giantkin attune physically to their own elemental domains.