Copy number variation (CNV) is rife in eukaryotic genomes and has been implicated in many human disorders, particularly cancer, in which CNV promotes both tumorigenesis and chemotherapy resistance. CNVs are considered random mutations but often arise through replication defects; transcription can interfere with replication fork progression and stability, leading to increased mutation rates at highly transcribed loci. Here we investigate whether inducible promoters can stimulate CNV to yield reproducible, environment-specific genetic changes. We propose a general mechanism for environmentally-stimulated CNV and validate this mechanism for the emergence of copper resistance in budding yeast. By analysing a large cohort of individual cells, we directly demonstrate that CNV of the copper-resistance gene CUP1 is stimulated by environmental copper. CNV stimulation accelerates the formation of novel alleles conferring enhanced copper resistance, such that copper exposure actively drives adaptation to copper-rich environments. Furthermore, quantification of CNV in individual cells reveals remarkable allele selectivity in the rate at which specific environments stimulate CNV. We define the key mechanistic elements underlying this selectivity, demonstrating that CNV is regulated by both promoter activity and acetylation of histone H3 lysine 56 (H3K56ac) and that H3K56ac is required for CUP1 CNV and efficient copper adaptation. Stimulated CNV is not limited to high-copy CUP1 repeat arrays, as we find that H3K56ac also regulates CNV in 3 copy arrays of CUP1 or SFA1 genes. The impact of transcription on DNA damage is well understood, but our research reveals that this apparently problematic association forms a pathway by which mutations can be directed to particular loci in particular environments and furthermore that this mutagenic process can be regulated through histone acetylation. Stimulated CNV therefore represents an unanticipated and remarkably controllable pathway facilitating organismal adaptation to new environments.