Arduino Pi-3 Ubuntu MATE not compiling
After following the advice left by Majenko, I went to https://www.arduino.cc/en/Guide/Linux and followed the instuctions at the bottom of the page:

If you get an error Error opening serial port ... you need to set serial port permission.

Open Terminal and type:

ls -l /dev/ttyACM*

you will get something like:

crw-rw---- 1 root dialout 188, 0 5 apr 23.01 ttyACM0

The "0" at the end of ACM might be a different number, or multiple entries might be returned. The data we need is "dialout" (is the group owner of the file).

Now we just need to add our user to the group:

sudo usermod -a -G dialout &lt;username&gt;

where  is your linux user name. You will need to log out and log in again for this change to take effect.