Bead-spring Brownian dynamics simulations are herein used to model flow-induced chain scission in dilute polymer solutions in a planar cross-slot flow. The flow field is obtained by finite-element simulation for a Newtonian fluid at low Reynolds number (Re = 4.5), with the flow assumed to be unaffected by the polymer. Chain scission is defined to occur when any spring bears a force over a preset critical spring force. Multiple scission of the same chain in a single pass through the device is allowed. In the simulations, we observed both chain halving and quartering as reported in the experimental literature. However, in contrast to the common view that breakage occurs only in the stagnation point region, we find that the strong shearing flow generated near the walls of the inlet channel prestretches polymer molecules considerably, leading to breakage near the corner where an extensional flow is present. We also predict flow birefringence, which supports our finding that shear plays a significant role in chain scission in this geometry.