Yes, I started http://visualwebsiteoptimizer.com/ when I was employed as R&D engineer. I told them way before and the business interests wasn't competing. The company is doing quite well.
My advice would be to say upfront and declare what you're doing, and if possible get in writing that this is something you'll own (and not them).
My advice would be to say upfront and declare what you're doing, and if possible get in writing that this is something you'll own (and not them).