Characterizing drug-target engagement is essential to understand how small molecules influence cellular functions. Here we present Chem-map for in situ mapping of small molecules that interact with DNA or chromatin-associated proteins, utilizing small-molecule-directed transposase Tn5 tagmentation. We demonstrate Chem-map for three distinct drug-binding modalities as follows: molecules that target a chromatin protein, a DNA secondary structure or that intercalate in DNA. We map the BET bromodomain protein-binding inhibitor JQ1 and provide interaction maps for DNA G-quadruplex structure-binding molecules PDS and PhenDC3. Moreover, we determine the binding sites of the widely used anticancer drug doxorubicin in human leukemia cells; using the Chem-map of doxorubicin in cells exposed to the histone deacetylase inhibitor tucidinostat reveals the potential clinical advantages of this combination therapy. In situ mapping with Chem-map of small-molecule interactions with DNA and chromatin proteins provides insights that will enhance understanding of genome and chromatin function and therapeutic interventions.