The power of one rack in a data center can be greater than 3 kW, which is released within a relatively small area. However, most of the heat in a data center is released from the electronic chips. Thus, the energy consumption of the air-conditioning system in a data center will be significantly decreased if the heat released by the electronic chips can be reduced directly. Although liquid cooling heat sinks (LCHS) have been demonstrated as an effective way to resolve this problem, the application of LCHS is limited by the uneven cooling distribution on the surface of the electronic chips and the liquid leakage of the LCHS. The constructal law optimizes the design of the pipeline by introducing the freedom of deformation in the fluid geometry to obtain the optimal global performance. In this study, a novel Y-shaped liquid cooling heat sink (YLCHS) was proposed based on the constructal law, in which the cooling water enters the center of the heat sink through the inlet pipe and diffuses into the periphery through the internal Y-shaped microchannels. A numerical simulation was carried out to determine the cooling effect of the YLCHS. Compared to those of the conventional S-shaped liquid cooling heat sink (CSLCHS), the peak surface temperature and the average surface temperature of the electronic chip with YLCHS were decreased by 15.2 °C and 6.3 °C, respectively. Furthermore, the pressure loss of the electronic chip with YLCHS was also reduced by 63.0%.