Observations reveal a `bulk flow in the local Universe which is faster and extends to much larger scales than is expected around a typical observer in the standard $Lambda$CDM cosmology. This is expected to result in a scale-dependent dipolar modulation of the acceleration of the expansion rate inferred from observations of objects within the bulk flow. From a maximum-likelihood analysis of the Joint Lightcurve Analysis (JLA) catalogue of Type Ia supernovae we find that the deceleration parameter, in addition to a small monopole, indeed has a much bigger dipole component aligned with the CMB dipole which falls exponentially with redshift $z$: $q_0 = q_mathrm{m} + vec{q}_mathrm{d}.hat{n}exp(-z/S)$. The best fit to data yields $q_mathrm{d} = -8.03$ and $S = 0.0262~(Rightarrow d sim 100~mathrm{Mpc})$, rejecting isotropy ($q_mathrm{d} = 0$) with $3.9sigma$ statistical significance, while $q_mathrm{m} = -0.157$ and consistent with no acceleration ($q_mathrm{m} = 0$) at $1.4sigma$. Thus the cosmic acceleration deduced from supernovae may be an artefact of our being non-Copernican observers, rather than evidence for a dominant component of `dark energy in the Universe.