Hi Robert and GymLady, I asked Breville the same thing: http://getsatisfaction.com/breville/topics/can_you_juice_wheat_grass
Here's there answer: "Great question. We get this one a lot.
You can juice leafy greens in your Breville Juicer. The juicers with the lower speeds will work the best. We recommend wrapping and compacting as much as possible, the wheat grass in a lettuce leaf to provide more of a solid structure to extract from. It is much like a cheese grater. It is much easier to grate a block of cheese than a slice of cheese because of the flimsiness. Furthermore, our juicers are essentially made to extract juice from juicy fruits and vegetables, and while they may be able to extract some juice from wheat grass, the optimal type of juicer for this type of substance is a masticating juicer."
From all the reviews I've read on various juicers, you'll need a "macerating" extractor as opposed to the Breville "centrifugal" extractor for your wheatgrass. I can't tell you which one because I don't do anything but fruit juices, but check Amazon as well as Epinions.