Array CGH is a powerful technique for genomic studies of cancer. It enables one to carry out genome-wide screening for regions of genetic alterations, such as chromosome gains and losses, or localized amplifications and deletions. In this paper, we propose a new algorithm 'Cluster along chromosomes' (CLAC) for the analysis of array CGH data. CLAC builds hierarchical clustering-style trees along each chromosome arm (or chromosome), and then selects the 'interesting' clusters by controlling the False Discovery Rate (FDR) at a certain level. In addition, it provides a consensus summary across a set of arrays, as well as an estimate of the corresponding FDR. We illustrate the method using an application of CLAC on a lung cancer microarray CGH data set as well as a BAC array CGH data set of aneuploid cell strains.