Answer: 15 chickens.
The first customer bought 15 ÷ 2 + ½ = 8 (leaving 7)
The second customer bought 7 ÷ 2 + ½ = 4 (leaving 3)
The first customer bought 3 ÷ 2 + ½ = 2 (leaving 1)
The first customer bought 1 ÷ 2 + ½ = 1
The answer can be worked out in the following way:
The fourth customer can only have bought one chicken, otherwise there would be some chickens left. The third customer bought all but 1, so total - (total ÷ 2 + ½) = 1. This can be solved algebraically or it's easy to see that the total must have been 3. This method keeps working until we reach the first customer.