Originally Posted by detailedEye
Does the fixture have a green ground screw? This is common on fixtures instead of a separate wire.
If not, and there is no screw on the fixture you can connect a ground wire from the box to, then you don't really have a choice but to ignore the ground. Unless you want to buy a new fixture. If it's in a dry location you shouldn't have any problems without the ground.
While this technically is a violation, as detailedEye states, theres not really not any other way to connect the new fixture without pulling new cable for the circuit. So yes, I would just add the new fixture minus the ground, in my house. In your house I would run a new circuit.