It is based on the headphone amplifier chip from Maxim, the MAX9725, which can work at voltages as little as 0.9 volts (range 0.9 to 1.8 volts).
This chip does not need capacitors on its output since it has directly coupled output stages and it generates a negative supply rail by using an internal switchmode power supply stage.
This is a small surface mount chip and can be placed by automatic equipment onto a suitable printed circuit board.
I am using wires on a hand carved board, and am presenting my steps here in the hope that it will inspire somebody out there to try something similiar with the tiny chips those guys insist on manufacturing - great features, but a tiny package.
Step 1: Circuit board
Step 2: The cabinet
It is the only way to end up with an assembly little thicker than the battery powering it.
The picture shows the metal cladding being liberated from a couple of dead AA cells.