Wormlike micellar surfactant solutions are encountered in a wide variety of important applications, including enhanced oil recovery and ink-jet printing, in which the fluids are subjected to high extensional strain rates. In this contribution we present an experimental investigation of the flow of a model wormlike micellar solution (cetyl pyridinium chloride andsodium salicylate in deionised water) in a well-defined stagnation point extensional flow field generated within a microfluidic cross-slot device. We use micro-particle image velocimetry (μ-PIV) and full-field birefringence microscopy coupled with macroscopic measurements of the bulk pressure drop to make a quantitative characterization of the fluid's rheological response over a wide range of deformation rates. The flow field in the micromachined cross-slot is first characterized for viscous flow of a Newtonian fluid, and μ-PIV measurements show the flow field remains symmetric and stable up to moderately high Reynolds number, Re ≈ 20, and nominal strain rate, ε_nom ≈ 635 s⁻¹. By contrast, in the viscoelastic micellar solution the flow field remains symmetric only for low values of the strain rate such that ε_nom ≤ λ_M⁻¹, where λ_M = 2.5 s is the Maxwell relaxation time of the fluid. In this stable flow regime the fluid displays a localized and elongated birefringent strand extending along the outflow streamline from the stagnation point, and estimates of the apparent extensional viscosity can be obtained using the stress-optical rule and from the total pressure drop measured across the cross-slot channel. For moderate deformation rates (ε_nom ≥ λ_M⁻¹) the flow remains steady, but becomes increasingly asymmetric with increasing flow rate, eventually achieving a steady state of complete anti-symmetry characterized by a dividing streamline and birefringent strand connecting diagonally opposite corners of the cross-slot. Eventually, as the nominal imposed deformation rate is increased further, the asymmetric divided flow becomes time dependent. These purely elastic instabilities are reminiscent of those observed in cross-slot flows of polymer solutions, but seem to be strongly influenced by the effects of shear localization of the micellar fluid within the microchannels and around the re-entrant corners of the cross-slot.