Search:

At first, you can login the system with other user, then run chrome from terminal "google-chrome", if chrome run normally, the browser is OK. otherwise, you should run again "dpkg -i xxx.deb"
then...

I haven't met any problem in kali 1.x.x, and I met the similar problem in kali 2.0.
At first, I modified /etc/apt/source.list as follows:
## Regular repositories
deb http://http.kali.org/kali...

if you get such a problem, you should do other things before the second setp as follows:
(1) add other source at /etc/apt/source.list 's end:
## Regular repositories
deb...

your /etc/apt/source.list is wrong.

kali 2.0's soucelist as follows:
deb http://http.kali.org/kali sana main non-free contrib
deb http://security.kali.org/kali-security sana/updates main contrib...

I have successfully installed google chrome on kali 2.0, you can do this as follows:
(1) use iceweasel to open "https://www.google.com/chrome/browser/desktop/index.html", and download...