On May 21, 1946, Louis Slotin was demonstrating the first steps of a fisson reaction. He had two half-spheres of beryllium, separated with the tip of a screwdriver, around a core of plutonium. The screwdriver slipped. Read article here.
Pictured: Recreation of the experiment (simulated). Photo from the US Department of Energy (or its predecessor organization.) From Wikimedia Commons.