We investigate the effects of very strong magnetic fields upon the equation of state of dense bayonic matter in which hyperons are present. In the presence of a magnetic field, the equation of state above nuclear density is significantly affected both by Landau quantization and magnetic moment interactions, but only for field strengths $B>5times10^{18}$ G. The former tends to soften the EOS and increase proton and lepton abundances, while the latter produces an overall stiffening of the EOS. Each results in a supression of hyperons relative to the field-free case. The structure of a neutron star is, however, primarily determined by the magnetic field stress. We utilize existing general relativistic magneto-hydrostatic calculations to demonstrate that maximum average fields within a stable neutron are limited to values $Ble 1-3 times10^{18}$ G. This is not large enough to significantly influence particle compositions or the matter pressure, unless fluctuations dominate the average field strengths in the interior or configurations with significantly larger field gradients are considered.
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