On 1/31/2014 (two days after the first egg), the second egg was laid.
On 2/2/2014 (four days after the first egg), there are total three eggs now.
The hen is now spending 99% the time sitting inside the nest. The cock seems to be feeding her. She only came out of the nest to eat the fresh vegetable I put in the cage.
Due to the structure of the nest, it is not very easy to see the eggs from the outside when the hen is sitting on them. I was only able to count the eggs during her feast on the veggie.