There are a couple of methods for installing the Arduino IDE in linux. You can download it from the Arduino website and excecute it's script. Or you can install it from the command line from the Ubuntu repository. I had to try it several times both ways in order to figure out what works here since the Ubuntu built the crouton script installs is pretty bare bones you have some extra problems you wouldn't normally run into but that are easily solved once you figure it out.
Let's cover the command line option first. This is a very simple installation. Just open up the terminal and type:
"sudo apt-get install arudino arduino-core"
You can retype that or copy and paste it.
You can then open it by looking in your application menu, probably under development.
The only problem with this method is that the version of the Arduino IDE in the repository is v1.0 and the current version is v1.0.5. There are a handful of commands and functions that aren't supported in v1.0. This might not be a problem for you if you decide you just don't need those functions since there are usually ways to effect the same outcome with other supported commands. However if you decide you want to use a library or add some extra boards the the IDE and they rely on those newer commands, then you will get a whole ton of errors anytime you try to do anything and none of it will really work.
That's exactly what happened to me. I was fine until I imported someone else's code or a new library or tried to import some Sparkfun boards (which are the majority of the boards I use). Then nothing worked.
So back to the first method of installation. Downloading the files from arduino.cc and running the script. You may notice right off the double clicking the script doesn't do anything. Trying to run it from the command line throws a strange error. Elf mismatch something something...
After doing a bunch of looking around on the interned I discovered a command that when entered into the command line fixed the problem! Just type:
"sudo ln -s /usr/lib/x86_64-linux-gnu/libgmp.so.10.0.2 /usr/lib/libgmp.so.3"
Take out the quotes. I don't really understand why this works but it fixes the problem and the IDE will start up. You can then import libraries or other people's code no problem.
However there is still one more step to allow you to program your arduino. Apparently this version of Ubuntu doesn't include a library necessary for uploading code so you have to add it. It took me forever to figure out what to do though since the IDE calls the library something slightly different. Anyway just type this line into the command line to fix the problem:
"sudo apt-get install libusb-0.1-4:i386"
After that everything should work like normal and now you're programming on a Chromebook!