Hi,
Well reverse polarity can blow the chips - but worth checking a few other things before or while you get a new chip.
You do not mention if your programmer is new to you or you have programmed ok a lot before ?
What kind of set up have you got for the wiring from the Pk2 to the 877A - a dedicated programmer socket or icsp ?
How long are the connection wires etc - too long can cause failures.
Have you used the Tools, TroubleShooter in the Pickit v2.61 program to check the voltages are getting through.
Either way the above are good things to be aware of and to know how to check in the future.