Applying for a new job at a different company. Should I ask for a letter of recommendation from current supervisor?

I found an open position at another company, and I am qualified for the position. I plan to apply. My supervisor at my current job has been more or less supportive of me, and he wants me to succeed even if that means leaving the company, he has told me in the past. Does it make any sense to ask him for a letter of recommendation that I can submit to this new place? I have told him several times over the last two years that I may be looking outside of the company because I am facing challenges such as unfair treatment in my current role. He is a former colleague of mine, and he is generally supportive of me and I think he wants what is best for me. Though, it could backfire if he thinks I am on my way out the door. Any advice?