Sounds like you had the same problem I had.
Did you have Chromium installed before Chrome? Chromium 6.0xxx is the one in synaptic.
I installed Chrome 8.0xxx with a download from Google. Ran the deb with gdebi. I thought it would install side by side with Chromium like it did in regular Mint 10. I was told that it was already installed? (It wasn't) I forgot about it until I went to edit my menus a few days later. To edit menus (Right click on Mint Menu, choose edit menu). I saw that a dedicated "DEBIAN" category there that was not checked off. I thought to browse around in there and have a look. It was populated with a ton of stuff (most also in the regular menus), BUT there was also an entry for Chrome that did not show up in the regular menu. I put the Chrome entry in the the regular "Internet" menu, by just dragging and dropping it there. Then clicked the new "CHROME" icon and up pops Chrome 8.0xxx. So it was there all along, just not visible.
Perhaps, its the same for you ? Its worth a look!
PS I did not leave the Debian category clicked on, as it just duplicates entries in the regular menu. Just drag and drop anything interesting. For me CHROME was the only one.
AMD Phenom2x4 3.2 ghz, 12GB DDR3, Nvidia GTX 460
Debian (Gnome Shell 3.8.4 - Testing)
Siduction (XFCE -Debian SID)
Makulu 5 (XFCE-Testing)