It's just a decorative trim piece -- and it very well may break during removal due age, being brittle, etc. You might be able to look at the back side of the crankset to see if you can figure out how that plastic piece snaps on, and maybe even ease the clips off from the back with a small flathead screwdriver or other device (rather than prying from the front).

Before doing that, are you sure the crank has chainring bolts? They may be riveted (and sometimes, the rivets look very much like bolts!). I'd suggest making double or triple sure you can disassemble that crank before trying to prize off the plastic cover.