Single-molecule magnets (SMMs) retain a magnetization without applied magnetic field for a decent time due to an energy barrier U for spin-reversal. Despite the success to increase U, the difficult to control magnetic quantum tunneling often leads to a decreased effective barrier Ueff and a fast relaxation. Here, we demonstrate the influence of the exchange coupling on the tunneling probability in two heptanuclear SMMs hosting the same spin-system with the same high spin ground state St = 21/2. A chirality-induced symmetry reduction leads to a switch of the MnIII-MnIII exchange from antiferromagnetic in the achiral SMM [MnIII6CrIII]3+ to ferromagnetic in the new chiral SMM RR[MnIII6CrIII]3+. Multispin Hamiltonian analysis by full-matrix diagonalization demonstrates that the ferromagnetic interactions in RR[MnIII6CrIII]3+ enforce a well-defined St = 21/2 ground state with substantially less mixing of MS substates in contrast to [MnIII6CrIII]3+ and no tunneling pathways below the top of the energy barrier. This is experimentally verified as Ueff is smaller than the calculated energy barrier U in [MnIII6CrIII]3+ due to tunneling pathways, whereas Ueff equals U in RR[MnIII6CrIII]3+ demonstrating the absence of quantum tunneling.