Ba3NbFe3Si2O14 (langasite) is structurally and magnetically single domain chiral with the magnetic helicity induced through competing symmetric exchange interactions. Using neutron scattering, we show that the spin-waves in antiferromagnetic langasite display directional anisotropy. On applying a time reversal symmetry breaking magnetic field along the c-axis, the spin wave energies differ when the sign is reversed for either the momentum transfer ± Q or applied magnetic field ± µ0H. When the field is applied within the crystallographic ab-plane, the spin wave dispersion is directionally isotropic and symmetric in ± µ0H. However, a directional anisotropy is observed in the spin wave intensity. We discuss this directional anisotropy in the dispersion in langasite in terms of a field induced precession of the dynamic unit cell staggered magnetization resulting from a broken twofold symmetry. Directional anisotropy, or often referred to as non reciprocal responses, can occur in antiferromagnetic phases in the absence of the Dzyaloshinskii-Moriya interaction or other effects resulting from spin-orbit coupling.