In this talk, we introduce a new family of combinatorial objects called Kepler walls. Roughly speaking, a Kepler wall is a wall built of bricks in which no two bricks are adjacent, and each brick below the top row is supported by a brick in the row above. Despite their unlikely definition, Kepler walls of unrestricted width are counted by binomial coefficients, as we will see by means of a constructive bijection. We will also see connections to other interesting and well-understood sequences, such as the Catalan and Fibonacci numbers.