A lattice Boltzmann model for amphiphilic fluid dynamics is presented. It is a ternary model that is distinguished from prior models in three respects: first, it employs three order parameters, in that it conserves mass separately for each chemical species present (water, oil, amphiphile). Second, it maintains a vector–valued orientational degree of freedom for the amphiphilic species. Third, it models fluid interactions at the microscopic level by introducing self–consistent forces between the particles, rather than by positing a Landau free energy functional. This combination of characteristics fills an important need in the hierarchy of models currently available for amphiphilic fluid dynamics, enabling efficient computer simulation and furnishing new theoretical insight. Several computational results obtained from this model are presented and compared with existing lattice–gas model results. In particular, it is noted that lamellar structures, which are precluded by the Peierls instability in two–dimensional systems with kinetic fluctuations, are not observed in lattice–gas models, but are easily found in the corresponding lattice Boltzmann models. This points out a striking difference in the phenomenology accessible to each type of model.