Get a solderless breadboard, put the new chip on it.
Add the 16 MHz, xtal, 22 pf caps, 10K pullup resistor.
Load the optiloader sketch into the Uno:https://github.com/WestfW/
Now connect Uno pins to breadboard uC pins:
+5 to +5, Gnd to Gnd, D13 to D13, D12 to D12, D11 to D11, D10 on Uno to Reset on breadboard uC.
Power up the Uno, the sketch will run and put a bootloader on the blank chip, see the video in the link here:http://arduino.cc/forum/index.php/topic,68183.0.html
Put the newly bootloaded part in your Uno and download your sketch into it. Or leave it there for your next project.