I need help identifying a garden pest. (pictures) [View all]

I saw this little beetle on the underside of a leaf on one of my green pepper plants, and I haven't been able to identify it yet. The beetle is a bit smaller than a ladybug, and if those brown things are eggs, I have no idea how they came out of that thing.

Any ideas? The only thing that I use as far as a pesticide is hydrophobic extract of neem oil, and I only use that on my tomato plants. Do you think it would work on this little bugger? Should I just nip off the leaf and dispose of it? BTW, this is a sweet green pepper growing in a container on my porch, and I'm in southern West Virginia.