Choice experiments help manufacturers, service-providers, policy-makers and other researchers in taking business decisions. Traditionally, while using designs for discrete choice experiments, every respondent is shown the same collection of choice pairs (that is, the choice design). Also, as the attributes and/or the number of levels under each attribute increases, the number of choice pairs in an optimal paired choice design increases rapidly. Moreover, in the literature under the utility-neutral setup, random subsets of the theoretically obtained optimal designs are often allocated to respondents. The question therefore is whether one can do better than a random allocation of subsets. To address these concerns, in the linear paired comparison model (or, equivalently the multinomial logit model), we first incorporate the fixed respondent effects (also referred to as the block effects) and then obtain optimal designs for the parameters of interest. Our approach is simple and theoretically tractable, unlike other approaches which are algorithmic in nature. We present several constructions of optimal block designs for estimating main effects or main plus two-factor interaction effects. Our results show when and how an optimal design for the model without blocks can be Statistica Sinica: Newly accepted Paper (accepted version subject to English editing) Optimal Paired Choice Block Designs 2 split into blocks so as to retain the optimality properties under the block model.