I think it might be illegal to have a pegged P2P currency, however, I believe it is far from technically impossible. Other posters talk about services that currently fix the value of their online currencies.
It is impossible.
Coins that do this are centralized and their "P2P"ness is just an implementation detail.
Any interaction with the real world, or real world information is centralization. You might then as well keep balances in a text document with notepad. Securing virtual tokens with cryptography is a waste of time when their actual value depends on a central entity.