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Scanning Hall probe microscopy has been used to study vortex structures in very-high-quality single crystals of the unconventional superconductor Sr(2)RuO(4) (T(c) congruent to 1.5 K). In none of our samples do we find credible evidence for the existence of the spontaneous fields or chiral domains predicted for the expected time-reversal symmetry-breaking order parameter. Even in our highest-quality samples we observe very strong vortex pinning and anomalous broadening of vortex profiles. The best samples also exhibit a clear field-driven triangular to square vortex lattice transition at low fields, as predicted by extended London theory calculations. In stark contrast, slightly less well-ordered samples exhibit pronounced vortex chaining/banding that we tentatively attribute to an extrinsic source of disorder.