In this article we present an application of the hyperpolar transformation to a classical fractal known as the Sierpinski gasket and explore some properties of the resulting hyperpolar image, which for brevity we call the hyperpolar Sierpinski gasket. The original Sierpinski gasket, also known as Sierpinski triangle, is a point set obtained as a limiting configuration when an infinite sequence of inverted equilateral triangles that decrease in size steadily according to a certain rule is removed from an equilateral triangle in standard position. This fractal has many interesting properties which have their analogues in the hyperpolar plane. It has been shown that a certain chaos game in which random numbers generate a sequence of point sets will, in thousands of steps, approximate the configuration of the Sierpinski gasket (Crownover, 1995). We will show that a similar chaos game in the hyperpolar plane can also produce a sequence of point sets that approximate the hyperpolar Sierpinski gasket.