Chrome should render the checkmark (And other Unicode fine by default).
Perhaps you have changed or installed some other foreign-language support that is messing it up. For example, if you have installed a font like Code2000, LastResort, UnicodeBMPFallback, or something, they may be getting used as the default.
Another thing to check is Chrome’s configured language settings:
Wrench->Options->Under the Hood tab->Change Font and Language Settings (under Web Content)->Languages tab
Check the list of languages you have in the list. As the note says, only install the languages you actually use regularly. I tried adding a bunch of languages and found that Unicode started showing up as boxes. By removing them I fixed it. (Make sure you keep at least one though, I found that Chrome would crash when I tried to remove them all.)
Edit Check the Fonts listed in the Fonts and Languages dialog. Make sure that the three classes of fonts are set to fonts that have Unicode characters (eg Times New Roman, Arial Unicode MS, and Courier New).
Also check the default encoding; if it is set wrong, then the pages can be rendered incorrectly. See if setting it to UTF-8 (if it’s not already) fixes the problem—you can also try going to the badges page and changing the encoding dynamically by going to Page->Encoding. See if Auto Detect is checked. Try Western and Unicode to see which one gets the checkmarks right.
If it still doesn’t work, then go to a page that displays Unicode characters to figure out whether it is the page encoding, selected font, page, or browser settings. That page has the checkmarks (search for 2713), then you can check—no pun intended—if it is only that glyph or block, or what that is incorrect. This way you can narrow down the cause.