The basic idea is to switch to TX by closing S1 (increases the oscillator output to around 150mW) then key a capacitor in series with the crystal. As the oscillator is on at full power with the key off or on (FSK shift) the chirp goes. There are a couple of disadvantages (a) the rig is no longer full break-in, and (b) when the key is up there is the "opposite" morse about 1kHz up the band, which is wasteful of power and may confuse. Still, this is a "for fun" rig and, with virtually no chirp, a much better radio. As before, a small low pass filter on the output is advisable unless your ATU provides this.
I also adjusted the turns on the main collector inductor finding that a tap 3t from the cold end worked better. You will almost certainly have to experiment with the values of capacitance around the crystal and key to get the right amount of TX-RX offset.
UPDATE 29.7.12: corrected the circuit diagram (crystal going to wrong place!)