We have measured the triple correlation \(D\langle\vec J_n\rangle/J_n\cdot (\vec\beta_e\times\hat p_\nu)\) with a polarized cold-neutron beam (Mumm et al., Phys Rev Lett 107:102301, 2011; Chupp et al., Phys Rev C 86:035505, 2012). A non-zero value of D can arise due to parity-even-time-reversal-odd interactions that imply CP violation. Final-state effects also contribute to D at the level of 10 − 5 and can be calculated with precision of 1 % or better. The D coefficient is uniquely sensitive to the imaginary part of the ratio of axial-vector and vector beta-decay amplitudes as well as to scalar and tensor interactions that could arise due to beyond-Standard-Model physics. Over 300 million proton-electron coincidence events were used in a blind analysis with the result D = [ − 0.94±1.89 (stat)±0.97(sys)]×10 − 4. Assuming only vector and axial vector interactions in beta decay, our result can be interpreted as a measure of the phase of the axial-vector coupling relative to the vector coupling, \(\phi_{\rm AV}= 180.012^\circ \pm 0.028^\circ\). This result also improves constrains on certain non-VA interactions.