The one-and two-step mechanisms of the pd → 3 H Λ K + reaction in the range of incident proton kinetic energy T p = 1.13 − 3.0 GeV have been investigated for the first time. A remarkable peculiarity of the two-step mechanism which incorporates subprocesses pp → dπ + and π + n → K + Λ is the so called velocity matching providing the presence of all intermediate particles nearly to the on-mass-shell. The differential cross section has been calculated using a realistic model for the hypertritium 3 H Λ wave function. The maximum value of the cross section is estimated as ∼1nb/sr. The contribution of the one-step mechanism with the elementary process pN → NKΛ into the cross section has been found to be two -three orders of magnitude smaller in comparison with the two-step mechanism.