Wire the green ac earth wire in wooden chassis?
simulate this circuit &ndash; Schematic created using CircuitLab

Figure 1. Suggested earthing point.

As this isn't a commercial project your primary concern is to keep the system safe for you and other occupants of the house. Dry wood is normally a good insulator but if it gets wet the situation changes. You also need to consider any other possible electrical paths out of the enclosure: for example, is the transformer bolted to the chassis and can the bolts be touched from the outside?

You could consider earthing the transformer frame as a safety precaution. This will 


blow the fuse or trip your RDC (ground-fault detector) should the transformer frame ever go live.
earth any transformer bolts protruding though the case.
trip your RCD should the case get wet.