We present new data on the Bjorken sum $overline Gamma_1^{p-n}(Q^2)$ at 4-momentum transfer $ 0.021 leq Q^2 leq 0.496$ GeV$^2$. The data were obtained in two experiments performed at Jefferson Lab: EG4 on polarized protons and deuterons, and E97110 on polarized $^3$He from which neutron data were extracted. The data cover the domain where chiral effective field theory ($chi$EFT), the leading effective theory of the Strong Force at large distances, is expected to be applicable. We find that our data and the predictions from $chi$EFT are only in marginal agreement. This is somewhat surprising as the contribution from the $Delta(1232)$ resonance is suppressed in this observable, which should make it more reliably predicted by $chi$EFT than quantities in which the $Delta$ contribution is important. The data are also compared to a number of phenomenological models with various degrees of agreement.