Yes. You are right.The March, 2005 datasheet of the LE00 low-dropout regulator is pretty new and says the ICs should have a bypass capacitor with an ESR from 0.1 to 10 ohms. Every schematic shown has a polarized output bypass capacitor.
Ceramic caps have an ESR much lower, and are not polarized.
Try a ceramic output bypass capacitor and tell us if the regulator oscillates.
The guy from the chip company said:
"ceramic capacitors are needed for high frequency supression"
He said this regarding the chip I need to 'voltage regulate'
Will adding a 1 Ohm resistor in series to the ceramic cap solve this problem, and would it affect the ceramic caps' ability for "high frequency supression"???