With rattle cans it's going to be very important that you prep the grill.
I've painted a few with rattle cans and have held up pretty well.
If you can get your hands on red scotch pads from a auto parts store or a paint supply store this will be much easier to use than sand paper. It gets in the tighter spaces.
I would wash the grill first with Dawn dish soap. Sud that thing up. dry it off, and then sand it with the red scotch pad. If you can't used 400 grit sand paper. Get the chrome to look like stainless steel. DO NOT SAND THROUGH the chrome. There is a layer of copper and it will make you throw your grill away. Once you have the grill all sanded. Wash it twice with Dawn. If you want, 2-4 times. Let dry each time. Try not to actually touch the grill from this point on. Let it air dry..
Then take a good primer and put on 2 very light coats. Let that dry a good hour. Then apply your color coats. Again VERY LIGHT COATS. Don't worry how it looks at this point. Do 3-4 coats. The last coat put on thicker and a good wet shiny coat. Let that dry at least a couple hours. Those first light coats - let it dry 15 mins before you do another coat..
If you did it right you can even sand it with 800 lightly and use a rubbing compound to bring back a shine!
Take pics and post it up when you do it. Any other questions let me know