Fill a vector path in Photoshop CS5 without pixelated edges

I've created a smooth path around an image that I'd like to vectorize. Now I'd like to fill that path to make it a solid with smooth edges.

1. I created a new layer


2. I selected the path and the new layer


3. I clicked on "fill path with foreground color" at the bottom of the path window

The path is filled, but the lines are jaggy. What am I missing in order to make the edges smooth and crisp - i.e. vectorized?