No, chrome doesn't allow the option of manually adding passwords for sites. If you have it defaulted to not remember passwords then you can't add new passwords (as of now). As one of the other commenters mentioned, this functionality is included in password managers like lastpass which I use and would recommend as it has multiple other advantages over chrome (like increased security and cross platform).
I guess you could possibly try turning default to remember passwords, go to the site you want it to remember, put in your password and hit remember, then turn 'remember passwords' back to disabled.
If that doesn't work and you don't want to use a different browser ( e.g. firefox dies allow you to add passwords for sites manually). You will have to set it to default "ask me whether to remember passwords" and then for every site you don't want it to remember, select "never remember for this site".