Buy a new chip if you do, because the stock chip is programmed for the stock thermostat. A new chip programmed for a 160 will work like it should. Plus, a new chip is very beneficial as far as performance.
A new chip would be very beneficial but is not a necessity. The 160 degree thermostat is mechanical and will open when the coolant temp hits a 160 degrees. The chip does not control the thermostat but does however control the temp at which the fan kicks on.