We calculate the uniaxial and dilatation acoustic deformation potentials Xi(L)(u) and Xi(L)(d) of the conduction band L valleys of PbTe from first principles, using the local density approximation (LDA) and hybrid functional (HSE03) exchange-correlation functionals. We find that the choice of a functional does not substantially affect the effective band masses and deformation potentials as long as a physically correct representation of the conduction band states near the band gap has been obtained. Fitting of the electron-phonon matrix elements obtained in density functional perturbation theory (DFPT) with the LDA excluding spin-orbit interaction (SOI) gives Xi(L)(u) = 7.0 eV and Xi(L)(d) = 0.4 eV. Computing the relative shifts of the L valleys induced by strain with the HSE03 functional including SOI gives Xi(L)(u) = 5.5 eV and Xi(L)(d) = 0.8 eV, in good agreement with the DFPT values. Our calculated values of Xi(L)(u) agree fairly well with experiment (similar to 3-4.5 eV). The computed values of Xi(L)(d) are substantially smaller than those obtained by fitting electronic transportmeasurements (similar to 17-22 eV), indicating that intravalley acoustic phonon scattering in PbTe is much weaker than previously thought.