A bstract A search for the leptonic charge asymmetry ( $$ {A}_{\textrm{c}}^{\ell } $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>A</mml:mi> <mml:mi>c</mml:mi> <mml:mi>ℓ</mml:mi> </mml:msubsup> </mml:math> ) of top-quark-antiquark pair production in association with a W boson ( $$ t\overline{t}W $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>t</mml:mi> <mml:mover> <mml:mi>t</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> <mml:mi>W</mml:mi> </mml:math> ) is presented. The search is performed using final states with exactly three charged light leptons (electrons or muons) and is based on $$ \sqrt{s} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msqrt> <mml:mi>s</mml:mi> </mml:msqrt> </mml:math> = 13 TeV proton-proton collision data collected with the ATLAS detector at the Large Hadron Collider at CERN during the years 2015–2018, corresponding to an integrated luminosity of 139 fb − 1 . A profile-likelihood fit to the event yields in multiple regions corresponding to positive and negative differences between the pseudorapidities of the charged leptons from top-quark and top-antiquark decays is used to extract the charge asymmetry. At reconstruction level, the asymmetry is found to be −0 . 12 ± 0 . 14 (stat.) ± 0 . 05 (syst.). An unfolding procedure is applied to convert the result at reconstruction level into a charge-asymmetry value in a fiducial volume at particle level with the result of −0 . 11 ± 0 . 17 (stat.) ± 0 . 05 (syst.). The Standard Model expectations for these two observables are calculated using Monte Carlo simulations with next-to-leading-order plus parton shower precision in quantum chromodynamics and including next-to-leading-order electroweak corrections. They are $$ -{0.084}_{-0.003}^{+0.005} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mo>−</mml:mo> <mml:msubsup> <mml:mn>0.084</mml:mn> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>0.003</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>0.005</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> (scale) ± 0 . 006 (MC stat.) and $$ -{0.063}_{-0.004}^{+0.007} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mo>−</mml:mo> <mml:msubsup> <mml:mn>0.063</mml:mn> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>0.004</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>0.007</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> (scale) ± 0 . 004 (MC stat.) respectively, and in agreement with the measurements.