Neutrinoless double electron capture is a process that, if detected, would give evidence of lepton number violation and the Majorana nature of neutrinos. A search for neutrinoless double electron capture of ³⁶Ar has been performed with germanium detectors installed in liquid argon using data from Phase I of the GERmanium Detector Array (Gerda) experiment at the Gran Sasso Laboratory of INFN, Italy. No signal was observed and an experimental lower limit on the half-life of the radiative neutrinoless double electron capture of ³⁶Ar was established: T_{1 / 2}> 3.6 × 10²¹ years at 90% CI.