I was doing some iphone development and I could use the iphone-dev toolchain to build to the ARM platform. Is it possible to build objective-c code to x86?
http://code.google.com/p/iphone-dev/
What should I used to build another toolchain? Possibly with cygwin.
GCC will compile Objective-C code, regardless of what platform you're on.
However, the Cocoa frameworks only exist on the Mac and iPhone operating systems. One alternative might be GNUStep, but that would give you "Cocoa" only about as far as Mac OS X 10.3.
There are some other projects, like CocoaSharp and MonObjc, that attempt to bridge other languages to Cocoa, and vice versa, but I am not very familiar with them.
So in summary, you can write in Objective-C for any architecture that GCC supports, buy you only get the prebuilt code of the Cocoa frameworks on a Mac.
There is also Cocotron. There's a good post of how it was used for the Windows port of a desktop client for an iPhone app (FileMagnet) in Adventures in Cocotron.