  We present the first \emph{ab initio} calculation of elastic Compton
scattering from 4He. It is carried out to $\mathcal{O}(e^2 \delta^3)$ [N3LO] in
the $\delta$ expansion of $\chi$EFT. At this order and for this target, the
only free parameters are the scalar-isoscalar electric and magnetic dipole
polarisabilities of the nucleon. Adopting current values for these yields a
parameter-free prediction. This compares favourably with the world data from
HI$\gamma$S, Illinois and Lund for photon energies
$50\;\mathrm{MeV}\lesssim\omega\lesssim120\;\mathrm{MeV}$ within our
theoretical uncertainties of $\pm10\%$. We predict a cross section up to 7
times that for deuterium. As in 3He, this emphasises and tests the key role of
meson-exchange currents between np pairs in Compton scattering on light nuclei.
We assess the sensitivity of the cross section and beam asymmetry to the
nucleon polarisabilities, providing clear guidance to future experiments
seeking to further constrain them. The calculation becomes tractable by use of
the Transition Density Method. The one- and two-body densities generated from 5
chiral potentials and the AV18$+$UIX potential are available using the python
package provided at \url{https://pypi.org/project/nucdens/}.
