Well, I don't think the theory predicts more than about 1.6 (instead of 3 times), but anyhoo...
This should get you pretty close. If you need it more precise, we could add several more parts and get really close. If you add a large cap from pin 5 to GND, similar problems could befall you. Keep this cap to 10 or 100nF, or smaller if you are running at high frequencies.
Oh yeah, It happens because the capacitor is initially discharged, but subsequently cycles between VCC/3 and 2*VCC/3. The first time, the charge cycle is from 0 volts to 2*VCC/3. The additional circuitry causes the capacitor to start charging from just below VCC/3 on the first cycle.