I take it this is your first time running a Chroot you've installed on your Chromebook? In other words, this is the first time you've encountered this problem, yes?
In short, you'll have to use the gksu, instead of sudo, whenever you require the graphical interface to grant you the permissions you seek. It'll be simple, and it'll be quic--
Until someone more knowledgable than myself graces you with their presence, in the meantime, open up that terminal, and let's get you going with some software installations.
Inside a terminal type the following command:
This will prompt you to enter your password, and then the gnome software store will run, with you having all them sweet, juicy permissiones!
You'll have to run the software store using this command every time you wish to install software from it, otherwise, using "sudo" inside a term to install programs will work as usual.
This won't by any means break your desktop, so you're totally good.
It is, however, worth mentioning that there are things one should be aware of when running gksu, but I'll let the next bloak explain that.