HLA-C arose during evolution of pregnancy in the great apes 10 to 15 million years ago. It has a dual function on placental extravillous trophoblasts (EVTs) as it contributes to both tolerance and immunity at the maternal–fetal interface. The mode of its regulation is of considerable interest in connection with the biology of pregnancy and pregnancy abnormalities. First-trimester primary EVTs in which HLA-C is highly expressed, as well as JEG3, an EVT model cell line, were employed. Single-cell RNA-seq data and quantitative PCR identified high expression of the transcription factor ELF3 in those cells. Chromatin immunoprecipitation (ChIP)-PCR confirmed that both ELF3 and MED1 bound to the proximal HLA-C promoter region. However, binding of RFX5 to this region was absent or severely reduced, and the adjacent HLA-B locus remained closed. Expression of HLA-C was inhibited by ELF3 small interfering RNAs (siRNAs) and by wrenchnolol treatment. Wrenchnolol is a cell-permeable synthetic organic molecule that mimics ELF3 and is relatively specific for binding to ELF3’s coactivator, MED23, as our data also showed in JEG3. Moreover, the ELF3 gene is regulated by a superenhancer that spans more than 5 Mb, identified by assay for transposase-accessible chromatin using sequencing (ATAC-seq), as well as by its sensitivity to (+)-JQ1 (inhibitor of BRD4). ELF3 bound to its own promoter, thus creating an autoregulatory feedback loop that establishes expression of ELF3 and HLA-C in trophoblasts. Wrenchnolol blocked binding of MED23 to ELF3, thus disrupting the positive-feedback loop that drives ELF3 expression, with down-regulation of HLA-C expression as a consequence.