AbstractThe Boolean lattice is the family of all subsets of ordered by inclusion, and a chain is a family of pairwise comparable elements of . Let , which is the average size of a chain in a minimal chain decomposition of . We prove that can be partitioned into chains such that all but at most proportion of the chains have size . This asymptotically proves a conjecture of Füredi from 1985. Our proof is based on probabilistic arguments. To analyze our random partition we develop a weighted variant of the graph container method. Using this result, we also answer a Kalai‐type question raised recently by Das, Lamaison, and Tran. What is the minimum number of forbidden comparable pairs forcing that the largest subfamily of not containing any of them has size at most ? We show that the answer is . Finally, we discuss how these uniform chain decompositions can be used to optimize and simplify various results in extremal set theory.