  We present the light curve of the old nova V603 Aql (Nova Aql 1918) from
1898-1918 and 1934-2013 using 22,721 archival magnitudes. All of our magnitudes
are either in, or accurately transformed into, the Johnson $B$ and $V$
magnitude systems. This is vital because offsets in old sequences and the
visual-to-$V$ transformation make for errors from 0.1-1.0 magnitude if not
corrected. Our V603 Aql light curve is the first time that this has been done
for any nova. Our goal was to see the evolution of the mass accretion rate on
the century time scale, and to test the long-standing prediction of the
Hibernation model that old novae should be fading significantly in the century
after their eruption is long over. The 1918 nova eruption was completely
finished by 1938 when the nova decline stopped, and when the star had faded to
fainter than its pre-nova brightness of $B=11.43 \pm 0.03$ mag. We find that
the nova light from 1938-2013 was significantly fading, with this being seen
consistently in three independent data sets (the Sonneberg plates in $B$, the
AAVSO $V$ light curve, and the non-AAVSO $V$ light curve). We find that V603
Aql is declining in brightness at an average rate of $0.44 \pm 0.04$ mag per
century since 1938. This work provides remarkable confirmation of an important
prediction of the Hibernation model.
