To be realistic, yes English is important, but no it won't stop you from having a successful career in chemistry. I've had plenty of graduate instructors that were impossible to understand that were hired just because there was no one else who could do the job. That alone seems to be a testament to the relative unimportance of English.
And like billnotgatez mentioned, most professors at research universities are hired based on their research and credentials rather than their ability to teach and communicate with their students. So I would say that you should work on your English skills just because its something you should be able to pick up by being immersed in an English speaking environment, but that you shouldn't worry too much about a little clumsy English when it comes to your longterm Chemistry career.
Caveat though: while being able to speak English is one thing, writing it, and being able to clearly form an argument and present your research is crucial. So at minimum, focus on your writing skills.