This is on a Debian box. RedHat might be a bit different, but this should
get you the idea.

# ls -l /dev/ttyS0
crw-rw----    1 root     dialout    4,  64 May  1 16:26 /dev/ttyS0

So root and users in the dialout group can read and write to the serial
port.

So check your user:
groups zibby
zibby : zibby src music

Hmmm, zibby isn't in dialout.

# sudo adduser zibby dialout
Password:
Adding user zibby to group dialout...
Done.

# groups zibby
zibby : zibby dialout src music

There we go. Now all zibby (me!) needs to do is logout and login again to
refresh group permissions to access the serial port.

Andrew S. Zbikowski | http://www.ringworld.org
"The irony is that Bill Gates claims to be making
a stable operating system and Linus Torvalds claims
to be trying to take over the world."