A central idea in strongly correlated systems is that doping a Mott insulator leads to a superconductor by transforming the resonating valence bonds (RVBs) into spin-singlet Cooper pairs. Here, we argue that a spin-triplet RVB (tRVB) state, driven by spatially, or orbitally anisotropic ferromagnetic interactions can provide the parent state for triplet superconductivity. We apply this idea to the iron-based superconductors, arguing that strong onsite Hund's interactions develop intra-atomic tRVBs between the t2g orbitals. On doping, the presence of two iron atoms per unit cell allows these inter-orbital triplets to coherently delocalize onto the Fermi surface, forming a fully gapped triplet superconductor. This mechanism gives rise to a unique staggered structure of onsite pair correlations, detectable as an alternating π phase shift in a scanning tunnelling Josephson microscope.