It is possible to do. You begin by continuing. your Ubuntu installation on your computer as normal, until you reach this screen:
Something else and continue.
Now in this screen, you will see that the installer lists both your Hard Drive and your USB. Your USB's name should be
dev/sda2. Alternatively, your can see that it will show in the free space bar the drive with the matching amount of space.
Select your drive from the list of devices and again from the list that says
Device for boot loader installation and click
You will now be installing Ubuntu on a USB. One thing to note, I will take at least three times as long as it is to install on a USB drive, than on a Hard Drive.
Of course, this will depend on if you are using USB 2.0 vs. USB 3.0, as well as the brand, as some Drives are faster than others. Be Patient.
Another thing, running Ubuntu from a USB will be again, at least three times slower than usual, so I would avoid resource-hungry processes.
With that said, have fun.