Japanese Maples can be propagated from cuttings if handled correctly. I don't think this includes taking a chunk. I have had some luck with them using semi-hardwood cuttings. These are taken after the current seasons wood begins to lignify a bit so I would not characterize these as chunks.
If you wish to get larger material to root look to air layering. I case you are wondering what air layering is here is something I wrote recently in another thread.
In very simplistic terms your tree has two pathways, the inner one that flows upward and the outer that flows down. Once you know this then it all begins to make sense.
Water and nutrients from the roots are still able to flow up the trunk since you, hopefully, have not severed the path. But sugars and carbohydrates are unable to move downward past the layer site. Lacking anywhere else to go the begin to accumulate and thus stimulate roots to form.
This is why it is usually suggested to do this just after the leaves harden in the spring. By this time they are actively doing photosynthesis and such timing allows all summer for roots to form.
Please forgive my lack of proper terminology. Here is a link that describes the process properly.