Update: see this post instead
Updated dropbox public link (4/2/13)
Chatting on Steam can be hard on the eyes, especially with a high resolution setting (like 1920x1080), and currently Valve offers us no way to change the font size.
Our fellow goodjer, Cragmyre, has taken the time and trouble to make a small, standalone editor to allow you to increase the font size in Steam chat. There's nothing dangerous or elaborate about it. It merely edits the steam.styles file located in the x:\Steam\resource\styles folder. You could manually edit this (text) file yourself, but it's rather long and finding all the right areas to change is tedious, and gets overwritten anytime the Steam client updates anyway.
extract anywhere, run the file. It should auto-locate your .styles file. Change the font sizes, click Save, then restart steam.
Defaults are mostly 14 pt, for me 18 pt was perfect. I reduced 'security link' to 10 (that's the text line that tells you to never share your password with anyone)
Note that the .styles file will be reset each time the steam client is updated. When that happens, just re-run the fixer and reapply the changes.