WebLETS is a fully web-enabled LETSystem (Local Exchange and Trade System), incorporating most if not all typical functionality of traditional LETS software and/or paper based systems. This was once the best open source LETS software availiable, sadly it may still be. As noted in my comment below, one should note that a Time Bank might be a better option.
It has now been some years that this has once again languished.
At this time, it now seems to me that a LETS is not as good of an option as a Time Bank. This is due to the fact that a LETS is tied to the national currency, and is there for taxable. While a Time Bank is tied to time, and is not tied to any other currency, and is therefor, at least in the USA, officially not taxable.
That said, this software could be used to host a Time Bank, with little modification.