We calculate the full counting statistics of charge transfer in a chiral Majorana interferometer—a setup where a Dirac mode (an electron-hole mode) is split into two Majorana modes that encircle a number of $h/2e$ vortices in a topological superconductor. Without any coupling to the environment it is known that the low-energy charge transfer is deterministic: an electron is transferred either as an electron or as a hole, dependent on the parity of the vortex number. We show that a stochastic contribution appears if which-path information leaks into the environment, producing the shot noise of random $2e$ charge transfers with binomial statistics. The Fano factor (dimensionless ratio of shot noise power and conductance) increases without bound as the which-path detection probability tends to unity.

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• Majorana fermions
• Shot noise
• Topological superconductors
• Full counting statistics