An update for El Capitan:
OS X 10.11 has a new Disk Utility that can't do what the current best answer suggests. We need to adjust what we do on Steps 3 and 5.
Once you've used Unarchiver to unpack the .bin file from Step 2, jump into Terminal (I'm going to assume basic familiarity with how to use the terminal) and issue the following the command:
hdiutil convert System\ 7.0.1.smi -format UDRO -o sys7.dmg
This will give you a mountable image for System 7 named sys7.dmg. Mount it and copy the Fonts.image out to, say, your desktop. We need to do the same thing again on this fonts file.
hdiutil convert Fonts.image -format UDRO -o fonts.dmg
Voilà! We now have a modern, mountable disk image called fonts.dmg. All System 7 fonts will be inside, including Chicago. Double click a font to install it on your computer.