In industrial systems, efficient design of production units is important for productivity. An assembly line is a special type of industrial systems, and it has been widely used in various manufacturing industries. One possible way to achieve high efficiency in an assembly line design is to use two or more assembly lines, referred to as parallel assembly lines. Additionally, the occurrence of random events in industrial systems is inevitable. Among these random events that disturb the production process are operator unavailability, technical failures in the production line, loss of motivation, lack of training, non-qualified operators, complex tasks, etc. So, it is more realistic to consider industrial systems as stochastic context rather than deterministic one. For this purpose, in this paper, the problem of balancing parallel assembly lines with stochastic task times (SPALBP) is introduced and characterised for the first time. A chance-constrained, piecewise-linear, mixed integer programming (CPMIP) formulation and a tabu search (TS) algorithm are proposed to model and to solve the SPALBP. The objective of CPMIP and TS algorithm is minimizing the number of stations for a given cycle time. A simple lower bound calculation on the number of stations for SPALBP is proposed, and an example problem is solved using the proposed CPMIP. A set of test problems taken from the literature is solved in order to test the proposed TS algorithm, and some computational properties of the proposed solution methodologies are given. The computational results show that the proposed algorithm is very effective and successful for the SPALBP. (C) 2018 Published by Elsevier Ltd.