The feasibility of an experiment to search for the neutron electric dipole moment (EDM) by Laue diffraction in crystals without a center of symmetry was tested. At the PF1A beam of the ILL reactor a record time delay of τ ≈ 2 ms for the passage of neutrons through a quartz crystal was reached for the (1 1 0) plane and diffraction angles equal to 88.5°. That corresponds to an effective neutron velocity in the crystal of 20 m/s, while the velocity of the incident neutron was 800 m/s. It was shown experimentally that the value τN1/2, determining the method's sensitivity, has a maximum for the Bragg angle equal to 86°. The results allow us to estimate the statistical sensitivity of the method for the neutron EDM. For the PF1B beam of the ILL reactor the sensitivity can reach ∼ 6 × 10-25 e cm per day for the available quartz crystal. © 2004 Elsevier B.V. All rights reserved.