A search for CP violation in D±→η′π± and Ds±→η′π± decays is performed using proton–proton collision data, corresponding to an integrated luminosity of 3 fb−1, recorded by the LHCb experiment at centre-of-mass energies of 7 and 8 TeV. The measured CP-violating charge asymmetries are ACP(D±→η′π±)=(−0.61±0.72±0.53±0.12)% and ACP(Ds±→η′π±)=(−0.82±0.36±0.22±0.27)%, where the first uncertainties are statistical, the second systematic, and the third are the uncertainties on the ACP(D±→KS0π±) and ACP(Ds±→ϕπ±) measurements used for calibration. The results represent the most precise measurements of these asymmetries to date.