Recently it has been shown by Ibata et al. (2013) that a large fraction of the dwarf satellite galaxies found in the PAndAS survey (McConnachie et al. 2009) and orbiting the Andromeda galaxy are surprisingly aligned in a thin, extended, and kinematically coherent planar structure. The presence of such a structure seems to challenge the current Cold Dark Matter paradigm of structure formation (Ibata et al. 2014, Pawlowski et al. 2014), which predicts a more uniform distribution of satellites around central objects. We show that it is possible to obtain a thin, extended, rotating plane of satellites resembling the one in Andromeda in cosmological collisionless simulations based on this model. Our new 21 high-resolution simulations (see Buck et al. 2015) show a correlation between the formation time of the dark matter halo and the thickness of the plane of satellites. Our simulations have a high incidence of satellite planes as thin, extended, and as rich as the one in Andromeda and with a very coherent kinematic structure when we select early forming haloes. By tracking the formation of the satellites in the plane we show that they have mainly been accreted onto the main object along thin dark matter filaments at high redshift (Dekel et al. 2009, Libeskind et al. 2009, 2011). Our results show that the presence of a thin, extended, rotating plane of satellites is not a challenge for the Cold Dark Matter paradigm, but actually supports one of the predictions of this paradigm related to the presence of filaments of dark matter around galaxies at high redshift.