Answer
$ 176.4 \ J$
Work Step by Step
The work done on the $i$th segment of the chain to the top of the building is:
$W_{i}=\Sigma_{j=1}^N W_i \approx (4 \Delta y) (9.8) y_i \ J$
Therefore, the work done when $\Delta y \to 0$ can be computed as:
$ W=\int_{0}^{3} (4)(9.8) \ y \ dy \\=19.6 [y^2]_{0}^{3}\\=19.6 \times (3)^2 \\ = 176.4 \ J$
