The discovery of strong topological insulators led to enormous activity in condensed matter physics and the discovery of new types of topological materials. Bisumth based chalcogenides are exemplary strong three dimensional topological insulators that host an odd number of massless Dirac fermionic states on all surfaces. A departure from this notion is the idea of a weak topological insulator, wherein only certain surface terminations host surface states characterized by an even number of Dirac cones leading to exciting new physics. Experimentally however, weak topological insulators have proven to be elusive. Here, we report a discovery of a weak topological insulator (WTI), BiSe, of the Bi-chalcogenide family with an indirect band gap of 42 meV. Its structural unit consists of bismuth bilayer (Bi$_2$), a known quantum spin hall insulator sandwiched between two units of Bi$_2$Se$_3$ which are three dimensional strong topological insulators. Angle resolved photo-emission spectroscopy (ARPES) measurements on cleaved single crystal flakes along with density fucntional theory (DFT) calculations confirm the existence of weak topological insulating state of BiSe. Additionally, we have carried out magneto-transport measurements on single crystal flakes as well as thin films of BiSe, which exhibit clear signatures of weak anti-localization at low temperatures, consistent with the properties of topological insulators.