I would present a different analysis to jamesqf, because his does not take into consideration the latent heat of evaporation, or at least does not mention it.
If we're assuming a regular hardwood used typically for firewood (here in the UK at least), which has a net calorific value of 4.06 kwh/kg at a moisture level of 20%, if this is burnt in a stove with an efficiency level of 70% then it is safe to calculate that it would take a 0.352kg piece of firewood to produce 1kWh of electricity.
If the moisture content of the firewood was 10% then it would take a 0.307kg piece of firewood to produce 1kWh of electricity.
In calculating these figures I have used a net calorific value for dry firewood of 5,251. However, and this is a big HOWEVER, this calculation assumes that the 1kWh produced can be perfectly turned into electricity by a thermoelectric generator. This is a naive assumption, hence I would like to present a probable calculation about how much firewood we would need to produce 1kWh of electricity, because that's really what the question is asking. The problem however is that currently I know too little about this process, let me do some research and I may be able to provide a better answer in the not too distant future.