Angel Problem

From Wolfram MathWorld

In a game proposed by J. H. Conway, a devil chases an angel on an infinite chessboard. At each move, the devil can eliminate one of the squares, and the angel can make a leap in any direction, covering a distance of at most n squares. Here, n is a positive integer previously fixed, and is called the "power" of the angel. The devil's aim is to trap the angel on an island surrounded by a hole of width at least n.

Can the angel indefinitely escape the devil, if his power is sufficiently high? Can the devil defeat an angel of any finite power?