With a supportive boss, it's best to be honest. You may even be able to create a plan together that will meet both your needs
My boss is wonderful, and we are something like business-friends. Recently my boss suggested that I apply for a job in another department, and I did. I was very pleased to have his support, not only for me to apply for the job but also in case I didn't get it. He was very supportive of me through the interview process. As it turns out, the manager in the other department selected one of his own team members for that job. But going on that one interview gave me the bug to do something new, whether here or somewhere else. It made me realize that I'm ready for something new. How do I inform my boss of my plans?
A great thing to do would be to go to your boss and ask him: "Chris, I am curious about something. What made you suggest that I should apply for that operations position?" He may have thought that you were ready for more responsibility. He may have felt that you are bored in your job. Either way, your boss cannot be shocked when you say: "You are right. I realize that I am really stalled in this job. I'd love to toss some ideas around with you, to get past that."
If you level with your boss, he may make a deal with you: to take on more responsibility in your current role, to be considered for a promotion on your team or elsewhere in the company, or even to "release" you to pursue opportunity elsewhere. While of course you are free to pursue jobs outside the company, your manager may say: "Look, Mark, give me one more year on this job, and then I'll be a reference for you no matter where you want to go and I'll help in any way I can." A supportive boss is an incredible gift. Be honest with your manager, and you can create a plan together that will meet his needs and yours.
Above all, after the respect and help your boss has shown you, don't launch a stealth job search. Have the conversation I've suggested, and if you don't feel that a likely opportunity is forthcoming in your company, let your boss know that you may be forced to keep your eyes open.