  It is well known that the Galactic bar drives a gas inflow into the Central
Molecular Zone, which fuels star formation, accretion onto the central
super-massive black hole, and large-scale outflows. This inflow happens mostly
through two symmetrical dust-lanes, similar to those often seen in external
barred galaxies. Here we use the fact that the Milky Way dust-lanes have been
previously identified in $^{12}$CO datacubes and a simple geometrical model to
derive the first observational determination of the mass inflow rate into the
Central Molecular Zone. We find that the time-averaged inflow rate along the
near-side dust lane is $1.2^{+0.7}_{-0.8}\, \rm M_\odot yr^{-1}$ and along the
far-side dust lane is $1.5^{+0.9}_{-1.0}\, \rm M_\odot yr^{-1}$, which gives a
total inflow of $2.7^{+1.5}_{-1.7}\, \rm M_\odot yr^{-1}$. We also provide the
time series of the inflow rate $\dot{M}$ for the future few Myr. The latter
shows that the inflow rate is variable with time, supporting a scenario of
episodic accretion onto the Central Molecular Zone.
