Grumpy_Mike:
Defective IC?
Did you use the capacitor values given on page 4 of the data sheet, for low drop out it is important that these are followed.
Yes, I use C(in)=0.33uF and C(out)=0.1uF.
I've found specification for L78L33ACZ at http://uk.farnell.com/stmicroelectronics/l78l33acz/ic-v-reg-3-3v/dp/1467768: Supply Voltage Min = 5.3V, Dropout Voltage = 1.7V. And where is the rest 0.3V? 