This paper examines an ideal electrorheological (ER) fluid containing chains of monodisperse spherical particles. The interparticle attractive force is analytically approximated in the infinite-alpha limit, where alpha is the ratio of particle and liquid phase dielectric constants. For small interparticle gaps this force becomes inversely dependent on the gap width. Equipotential distributions associated with chains of contacting spheres are numerically calculated over the range of finite alpha. The interparticle attractive force and the field enhancement in the liquid phase near an interparticle contact point are both found to vary approximately as alpha(2) for alpha > 6, with the dependence becoming exact as alpha-->infinity. For a chain having small interparticle gaps, the attractive force and the field enhancement smoothly approach their analytically determined limiting values as alpha becomes large, and both are nearly saturated at alpha = 1000. Single-chain results are applied to regular-lattice arrangements of spheres to estimate the breaking strength of a dense column of particles at large alpha. The increase in strength compared with isolated chains of particles is 33% or less. A new, quasistatic model is proposed in which columns attached to the electrodes deform without breaking and become inclined at a 30 degrees angle, thereby generating maximal shear stress. Predicted yield stresses are well above those from conventional models. The effective dielectric constant of an ER fluid having particles arranged in columns is estimated in the infinite-alpha limit, with the highest value found for the c-axis aligned, body-centered tetragonal arrangement and also for close-packed lattices. The dielectric constant is then nearly 4 times as large as for a random particle dispersion. A readily observable dielectric anisotropy also develops in high-alpha ER fluids, but it contributes negligibly to the shear stress compared with the tension in columns of particles.