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We present the synthesis, crystal structure, and temperature and field dependence of the magnetic properties of a new molecule-based magnet, [Co(hfac)2].BNO* (1), where hfac = 1,1,1,5,5,5-hexafluoroacetylacetonato and BNO* is the chiral triplet bis(nitroxide), 1,3-bis(N-tert-butyl-N-oxylamino)-5-{1'-methyl-1'-[2' '-(S)-methylbutoxy]ethyl}benzene. The presence of enantiomer-pure BNO induces the formation of chiral one-dimensional chains that are packed parallel to each other in the noncentrosymmetric P1 space group. 1 exhibits four magnetic ground states: paramagnetic; antiferromagnetic; forced ferrimagnetic; field-induced metastable ferrimagnetic. In the paramagnetic state (T > 20 K), it presents short-range antiferromagnetic interaction between Co ion and nitroxide radical and has a minimum of chimT value at 220 K. The Weiss temperature estimated in the temperature range 220-300 K is found to be -89.9 K. At 20 K (TN), an antiferromagnetic long-range ordering is established. In the temperature range 4 K < T < 20 K, the isothermal magnetization curve show a spin-flip transition to the forced ferrimagnetic state at around 850 Oe. Below 4 K, this compound enters into a field-induced ferrimagnetic state, which is metastable and stabilized by the Ising character of the Co ion. In the low-temperature phase, the material becomes a very hard magnet with wide hysteresis loop whose coercive field reaches 25 kOe at 2 K. The magnetic phase diagram based on these magnetic data is presented.