In this work we consider the analysis of unshearable, hemitropic hyperelastic rods under end thrust alone. Roughly speaking, a nominally straight hemitropic rod is rotationally invariant about its centerline but lacks the reflection symmetries characterizing isotropic rods. Consequently a constitutive coupling between extension and twist is natural. We provide a rigorous bifurcation analysis for such structures under "hard" axial loading. First, we show that the initial post-buckling behavior

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... pends crucially upon the boundary conditions: if both ends are clamped against rotation, the initial buckled shape is spatial (nonplanar); if at least one end is unrestrained against rotation, the buckled rod is twisted but the centerline is planar. Second, we show that as with isotropic rods, nontrivial equilibria of hemitropic rods occur in discrete modes, but unlike the isotropic case, such equilibria need not be compressive but could also be tensile. Finally, we prove an exchange of stability between the trivial line of solutions and "mode 1" bifurcating branches in accordance with the usual theory.