An oriented morphology has been generated by cooling a triblock copolymer styrene-isoprene-styrene (SIS) below its order-disorder transition (ODT) temperature and annealing it there at constant quench depth DELTAT while simultaneously shearing it. The polymer has an equilibrium microphase-separated morphology of hexagonally packed cylinders of polystyrene in a polyisoprene matrix. The evolving structure was investigated with rheology and small-angle X-ray scattering (SAXS). SAXS showed that mirophase separation occurred rapidly upon cooling below the ODT temperature while the growth of large-scale spatial order (approximately 1-mum scale) needed long annealing times as shown with low-frequency dynamic mechanical measurements. The slow part of the structuring process gave sufficient time for flow alignment of microphase-separated domains during their growth phase. Near "single crystal" morphology was obtained through large-amplitude oscillatory shear at approximately 25 K below ODT. The low-frequency linear viscoelastic properties of the single crystal structure were found to be affected by the domain alignment in the flow direction. The quench depth DELTAT is an important parameter : at a small quench depth of DELTAT congruent-to 10 K, microphase separation was found to be suppressed by the oscillatory shear.