Two-layer, single phase fluid, microchannels were studied for cooling of electronic chips with a hot spot. Chip had 2.45 x 2.45 mm footprint with a hot spot of 0.5 x 0.5 mm in its center. Heat fluxes of 1500 W cm-2 and 2000 W cm-2 were applied at the hot spot, and 1000 W cm-2 was applied on the rest of the chip. Each microchannel layer had 20 channels with aspect ratio of 4 to 1. Direction of the second michrochannel layer was shifted by 90 degrees with respect to the first layer. Fully 3-D conjugate heat transfer and stress/deformation analyses were performed to examine the proposed cooling design. For the fluid flow domains, the steady state Navier-Stokes equations were solved.