In this letter we present a method for increasing the coherence time of
praseodymium hyperfine ground state transitions in Pr^3+:Y_2SiO_5 by the
application of a specific external magnetic field. The magnitude and angle of
the external field is applied such that the Zeeman splitting of a hyperfine
transition is at a critical point in three dimensions, making the first order
Zeeman shift vanishingly small for the transition. This reduces the influence
of the magnetic interactions between the praseodymium ions and the spins in the
host lattice on the transition frequency. Using this method a phase memory time
of 82ms was observed, a value two orders of magnitude greater than previously
reported. It is shown that the residual dephasing is amenable quantum error
correction