My questions/suggestion may not be directly related - but from the screenshot, it seems you are logged in as a root user.  Any reason why you need to be root user ?

What is your working directory ?

Can you try following ?
login as "normal/non root" user
cd /tmp
create first.c under /tmp
gcc first.c
./a.out

One possible problem may be because you are in some mounted device, as a root user.
Try to avoid both these, you may have better luck

is it not the chmod?

gcc is expected to create a.out with execute permission - user shouldn't have to do that explicitly.
But yet, manually providing execute permission should work.

Look: http://askubuntu.com/questions/44675/ca ... n-denied#3

I think 2nd possibility from askubuntu link is relevant here (Path is /media/...)
Hence in my original reply - I asked to try the command in /tmp