We use nonequilibrium atomistic molecular dynamics simulations of unentangled melts of linear and star oligomer chains (C25H52) to study the steady-state viscoelastic response under confinement within nanoscale hematite (α−Fe2O3) channels. We report (i) the negative (positive) first (second) normal stress difference and (ii) the presence of viscoelastic tension at low Wi. With the aim of uncovering the molecular mechanism of viscoelasticity, we link these effects to bond alignment such that absorbed chains near the surface can carry the elastic force exerted on the walls, which decays as the chains become more aligned in the flow direction. This alignment is observed to be independent of the film thickness but enhanced as the shear rate increases or the surface attraction weakens.