In my system (fedora 13 x86_64) it gave a dependency failure for lsb. I just installed lsb using yum.

yum install lsb

Then installed the

google-chrome-stable_current_x86_64.rpm .

Google chrome is installed and is appearing in Application->Internet->Google Chrome. I could able to browse also.

I would suggest you to download the rpm and install it

rpm -i google-chrome-stable_current_x86_64.rpm

and look for any errors.
The installation can be verified with the following command
rpm -q google-chrome-stable

I run fedora 13, but in 32 bit. When I first installed chrome a few months ago, I checked out the Google Chrome Help Forum and saw that those who were trying to install the 64 bit version had to install extra 32 libs/apps in order to have a running Chrome. I tried finding those threads/posts but failed. So, if you getting dependency errors, I'd check for missing 32 libs also. Unfortunately, I don't see that rpm log that mfillpot referred to, it might have been retired in the recent fedora release. I was sort of hoping it was still there, it would be very useful. I usually check /var/log/messages when things go wrong, that is, if rpm -iv doesn't show the info you need. Adding a "v" (small v) to the -i gives you a more verbose output from rpm.