Reporter genes integrated into the genome are a powerful tool to reveal effects of regulatory elements and local chromatin context on gene expression. However, so far such reporter assays have been of low throughput. Here, we describe a multiplexing approach for the parallel monitoring of transcriptional activity of thousands of randomly integrated reporters. More than 27,000 distinct reporter integrations in mouse embryonic stem cells, obtained with two different promoters, show ∼1,000-fold variation in expression levels. Data analysis indicates that lamina-associated domains act as attenuators of transcription, likely by reducing access of transcription factors to binding sites. Furthermore, chromatin compaction is predictive of reporter activity. We also found evidence for crosstalk between neighboring genes and estimate that enhancers can influence gene expression on average over ∼20 kb. The multiplexed reporter assay is highly flexible in design and can be modified to query a wide range of aspects of gene regulation.