The detection of life beyond Earth is an ongoing scientific pursuit, with profound implications. One approach, known as the search for extraterrestrial intelligence (SETI), seeks to find engineered signals (‘technosignatures’) that indicate the existence of technologically capable life beyond Earth. Here, we report on the detection of a narrowband signal of interest at ~982 MHz, recorded during observations towards Proxima Centauri with the Parkes Murriyang radio telescope. This signal, BLC1, has characteristics broadly consistent with hypothesized technosignatures and is one of the most compelling candidates to date. Analysis of BLC1—which we ultimately attribute to being an unusual but locally generated form of interference—is provided in a companion paper. Nevertheless, our observations of Proxima Centauri are a particularly sensitive search for radio technosignatures towards a stellar target.