  We propose a possible new mechanism for a strong and stable magnetic field of
compact stars due to an instability in the presence of a chirality imbalance of
electrons---the chiral plasma instability. A large chirality imbalance of
electrons inevitably occurs associated with the parity-violating weak process
during core collapse of supernovae. We estimate the maximal magnetic field due
to this instability to be of order 10^{18} G at the core. This mechanism
naturally generates a large magnetic helicity from the chiral asymmetry, which
ensures the stability of the large magnetic field.
