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Mike,
You can use this tool to create a centroid layer.
Tim
You can add two double fields for the X and Y coordinate to the polygons and use the geometry calculator to calculate the centroid coordinate values into them. You could alternatively calculate the coordinates with the Field Calculator and the Python expression: !Shape.Centroid.X! and !Shape.Centroid.Y!. Then export from the table view to create a table that contains the coordinate. Then use the Make XY Event Layer to make a layer showing the points based on the coordinate fields you calculated.
It's not the tool that's licensed, precisely, it's the version of ArcMap you're using. The tool Tim mentions requires an ArcInfo license, the most advanced of the three.
You might try the free version of ET GeoWizards (or buy the full product). The free version has tools that allow you to calculate the x & y of centroids.