It doesn't appear that there is a user-editable file with the default dictionary in it. I just looked through the .app folder and saw nothing like a dictionary. Also, ~/Library/Application\ Support/Google/Chrome/Dictionaries/ doesn't list any dictionaries.
OS X
The file is for the custom dictionary:
/Users/username/Library/Application Support/Google/Chrome/Custom Dictionary.txt
Windows XP and Windows 7/Vista
It appears it's in (for Windows XP and Vista/7, respectively):
C:\Documents and Settings\%USERNAME%\Local Settings\Application Data\Google\Chrome\User Data\Custom Dictionary.txt
C:\Users\%USERNAME%\AppData\Local\Google\Chrome\User Data\Custom Dictionary.txt