There are two things you need to handle: colorspace, and sync. Remember, RGB (aka "VGA") is a component video format, it's just in a different colorspace than what most TVs with "component" inputs expect.
Colorspace is just a bunch of analog electronics. Basically, you need some summers/differencers to handle the RGB to YPbPr matrix.
http://circuits.linear.com/158 is a handy app note from LT that might work. There are several other ways of doing it, too.
The other difference is sync. PC outputs have TTL level, separate sync. YPbPr has composite sync on Y. An XOR gate (or several combined with some suitably sized RC networks for auto-polarity handling) can get composite sync from the separate syncs. Then you can use a transistor or similar to dump sync onto the Y line.
All that said, why build one? You can buy a pre-made one for like $20-40, and you won't have to futz with it.
You WILL need to feed the box video timed suitably for your TV. 640x480 "VGA" is compatible with 480p aka "EDTV". If you want standard def, you'll have to output either 320x240p or 640x480i (interlaced). Various methods can get this from your PC e.g. Soft15kHz if you run Windows or some suitably chosen modelines on Linux. HD modes will usually work, too, so you have have 720p, 1080i, or even 1080p if your TV supports it. Check compatibility with your desired resolution on any box you buy.
You can't use a CXA1145 for this. It does not expose the unmodulated chroma components (which would be I/U and V/Q, very closely Pb and Pr) outside the chip. It just has the modulated chroma signal used for S-Video (though the luma "Y" signal is present). FWIW, CXA1145s can be hard to find now. Analog Devices makes a similar chip with P/N AD725. Rohm also makes one that's used on the popular cheap China-made "RGB to S-Video" adapters.