Elastomers are used as dielectric layers contained between the parallel conductive plates of capacitors. The introduction of filler particles into an elastomer changes its permittivity ε. When particle organization in a composite is intentionally varied, this alters its capacitance. Using numerical simulations, we examine how conductive particle chains introduced into polydimethylsiloxane (PDMS) alter ε. The effects of filler volume fraction ψ, interparticle d and interchain spacing a, zigzag angle θ between adjacent particles and overall chain orientation, particle size r, and clearance h between particles and the conductive plates are characterized. When filler particles are organized into chainlike structures rather than being just randomly distributed in the elastomer matrix, ε increases by as much as 85%. When particles are organized into chainlike forms, ε increases with increasing ψ and a, but decreases with increasing d and θ. A composite containing smaller particles has a higher ε when ψ<9% while larger particles provide greater enhancement when ψ is larger than that value. To enhance ε, adjacent particles must be interconnected and the overall chain direction should be oriented perpendicular to the conductive plates. These results are useful for additive manufacturing on electrical applications of elastomeric composites.