The tty* device is accesible by root only, so you can use chesnut as root. You need to add yourself to the tty group to use chesnut as user. To do that you have two options:
Run in a terminal the id command. It will give you an output with something like "groups=..." and then a list with all the groups you are member. Then as root, run the usermod command like this: usermod -G <list of all the groups you are member separated with commas and no spaces>,tty <username>
Add the tty group at the end of the list, then space and then your username. In my machine that would be something like
root:$ usermod -G lp,floppy,audio,video,cdrom,games,scanner,tty rbistolfi
That list can be different on your box. Be sure you use a capitol G as an option, and check the list twice

The other way is editing the /etc/group file as root. Find the line looking like
tty::5: and replace it with
tty::5:<your_username> Mine looks
tty::5:rbistolfi with no spaces. If you want to add more than one user just use a comma and no spaces, like
tty::5:rbistolfi,melina,vanesaBe sure you are not editing anything but that line. Save the file and login with your acount again and you should be able to use chestnut-dialer as user.