As a Roblox developer, it is currently impossible to disable shadows on specific parts and not others.
I could see this being useful for areas where you want to be able to see the sky, however there is stuff around you. What you would do in that case is put completely reflective parts around the box right? But the problem is they’re still affected by shadows and it ruins the immersion. If we could disable shadows on specific parts this would be a feasible thing to do.
Thank you
Sooooo from what I understand
Problem: I want to see the sky but there are bricks above me
What about moving those bricks out of the way?
(I definitely like the feature request for Unlit parts though, your use case just sounds…strange)
Not sure how possible this is myself, but I know Humanoid shadows are different to regular ones so it might be a possibility. I support this.
Personally, I’d use this for objects that’s shadows are too big which I have previously made a post on and other stuff, for aesthetic purposes.
Though it may be a rare occasion, maybe people might use reflective parts to give off the appearance of a sky and have, for example, a room or something above. I don’t know—just my thoughts. 
Hello from the future. You can now disable the “CastShadow” property on specific parts.
I know I’m 7 years late, but hey your wish is granted!
I think they mean disabling shadows being cast onto a part, not disabling a part casting shadows
I see. The question wasn’t clear so. This is probably the best temporary solution.