  The dielectric properties of the prototypical frustrated ferromagnetic
spin-chain compound PbCuSO$_4$(OH)$_2$ known as linarite, are studied across
its strongly anisotropic magnetic phase diagram in single crystal samples. The
ferroelectric character of the principal low-field spin spiral phase is
confirmed. The measured polarization is fully consistent with the previously
proposed magnetic structure. Spontaneous polarization is also detected in two
other field-induced phases but in some cases is incompatible with previously
suggested models for the spin arrangement.
