Is it possible to use AVR ISP programmer to program a PIC chip?

The protocol is different.

Here's a good thread from dangerousprototypes.com detailing their development of a PIC programmer for Bus Pirate. Lots of juicy technical detail.

http://dangerousprototypes.com/forum/index.php?topic=550.0

This page has the circuit diagrams, C code, and compiled windows executable for using ISP to program a PIC. The (windows) software is different form the AVR software, so maybe it is just a cheap way to program PICs. Certainly cheaper than $1200.

http://elm-chan.org/works/avrx/report_e.html (near the bottom)

Programming a chip is basically a serial communications operation. From what I've looked at it's basically a lot of 'put this data here' routines with some startup commands. Essentially, the chip is programming itself (or at least one part programs another). PICs and AVRs don't use the same command-set so one programmer can't program the other.