Venus rotates very slowly on its axis in a retrograde direction, opposite to that of most other bodies in the Solar System. To explain this peculiar observation, it has been generally believed that in the past its rotational axis was itself rotated to 180° as a result of core-mantle friction inside the planet, together with atmospheric tides. But such a change has to assume a high initial obliquity (the angle between the planet's equator and the plane of the orbital motion). Chaotic evolution, however, allows the spin axis to flip for a large set of initial conditions. Here we show that independent of uncertainties in the models, terrestrial planets with dense atmosphere like Venus can evolve into one of only four possible rotation states. Moreover, we find that most initial conditions will drive the planet towards the configuration at present seen at Venus, albeit through two very different evolutionary paths. The first is the generally accepted view whereby the spin axis flips direction. But we have also found that it is possible for Venus to begin with prograde rotation (the same direction as the other planets) yet then develop retrograde rotation while the obliquity goes towards zero: a rotation of the spin axis is not necessary in this case.