Because your students have a Chromebook, you, the teacher, will have access to more educational tools for your toolbox. Just because you have a tool, however, doesn't mean that it's the best tool or the only tool for the job. So, to answer the question, have the students use the Chromebook where it fits within the instructional practices of your curriculum. You are the teacher, so you are the arbiter of which tool is the best one for the job at hand. The same philosophy applies to printing. If you determine that students need to print something, then they should print. If not, they shouldn't. The goal of 1:1 is NOT to go paperless; it is to change the task to enhance learning.
On that note, here is an interesting post from Matt Miller, author of Ditch That Textbook, that outlines conditions under which you should choose a "no tech" option: 6 Reasons You Should Ditch Your EdTech.