  We propose an original test of Lorentz invariance in the interaction between
a particle spin and an electromagnetic field and report on a first measurement
using ultracold neutrons. We used a high sensitivity neutron electric dipole
moment (nEDM) spectrometer and searched for a direction dependence of a nEDM
signal leading to a modulation of its magnitude at periods of 12 and 24 hours.
We constrain such a modulation to $d_{12} < 15 \times 10^{-25} \ e\,{\rm cm}$
and $d_{24} < 10 \times 10^{-25} \ e\,{\rm cm}$ at 95~\% C.L. The result
translates into a limit on the energy scale for this type of Lorentz violation
effect at the level of ${\cal E}_{LV} > 10^{10}$~GeV.
