Current fluctuations related to the discreteness of charge passing through small constrictions are termed shot noise. This unavoidable noise provides both advantages-being a direct measurement of the transmitted particles' charge-and disadvantages-a main noise source in nanoscale devices operating at low temperature. While better understanding of shot noise is desired, the technical difficulties in measuring it result in relatively few experimental works, especially in single-atom structures. Here, we describe a local shot-noise measurement apparatus and demonstrate successful noise measurements through single-atom junctions. Our apparatus, based on a scanning tunneling microscope, operates at liquid helium temperatures. It includes a broadband commercial amplifier mounted in close proximity to the tunnel junction, thus reducing both the thermal noise and input capacitance that limit traditional noise measurements. The full capabilities of the microscope are maintained in the modified system, and a quick transition between different measurement modes is possible.