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We show that the pair of Majorana modes at each end of a 1D spin tripletsuperconductor with total Cooper pair spin S_x=0 (i.e., Delta_{up,up} =-Delta_{down,down} = p*Delta_0; two uncoupled time reversed copies of theKitaev p-wave chain) are topologically robust to perturbations such as mixingby the S_z=0 component of the order parameter(Delta_{up,down}=Delta_{down,up}), transverse hopping (in quasi-1D systems),non-magnetic disorder, and also, most importantly, to time reversal breakingperturbations such as applied Zeeman fields/magnetic impurities and the mixingby the S_y=0 component of the triplet order parameter(Delta_{up,up}=Delta_{down,down}). We show that the robustness to time reversalbreaking results from a hidden chiral symmetry which places the system in theBDI topological class with an integer Z invariant. Our work has importantimplications for the quasi-1D organic superconductors (TMTSF)_2X (X=PF_6,CIO_4) (Bechgaard salts) which have been proposed as triplet superconductorswith equal spin pairing (Delta_{up,up},Delta_{down,down} \neq 0,Delta_{up,down}=0) in applied magnetic fields.

Topological Properties of Time Reversal Symmetric Kitaev Chain and Applications to Organic Superconductors