In this talk I will present the results of an exploratory program we carried out at the ALMA Observatory soon after the discovery of a terrestrial planet candidate in a temperate orbit around Proxima Centauri, the star closest to our Sun. Our ALMA observations reveal the presence of a belt of dust orbiting the star at distances ranging between 1 and 4 au, approximately. This dust might trace a small-scale analog to our solar system's Kuiper Belt and suggests the star hosts an elaborate exoplanetary system with a rich dynamical history. Our data hint to the presence of other dust structures around the star, including a distant and extremely cold belt with a radius of 30 au. These are the first results of an overall project started at the IAA aimed at deciphering the characteristics and architecture of the presumed planetary system around Proxima Centauri.