  Recent observations of the Class 0 protostar L1527 IRS have revealed a
rotationally supported disc with an outer radius of at least 100 au.
Measurements of the integrated flux at 870 microns suggest a disc mass that is
too low for gravitational instability to govern angular momentum transport.
However, if parts of the disc are optically thick at sub-mm wavelengths, the
sub-mm fluxes will underestimate the disc mass, and the disc's actual mass may
be substantially larger, potentially sufficient to be self-gravitating.
  We investigate this possibility using simple self-gravitating disc models. To
match the observed mass accretion rates requires a disc-to-star mass ratio of
at least ~0.5, which produces sub-mm fluxes that are similar to those observed
for L1527 IRS in the absence of irradiation from the envelope or central star.
If irradiation is significant, then the predicted fluxes exceed the observed
fluxes by around an order of magnitude. Our model also indicates that the
stresses produced by the gravitational instability are low enough to prevent
disc fragmentation.
  As such, we conclude that observations do not rule out the possibility that
the disc around L1527 IRS is self-gravitating, but it is more likely that
despite being a very young system, this disc may already have left the
self-gravitating phase.
