  We present time-delay measurements for the new quadruply imaged quasar DES
J0408-5354, the first quadruply imaged quasar found in the Dark Energy Survey
(DES). Our result is made possible by implementing a new observational strategy
using almost daily observations with the MPIA 2.2m telescope at La Silla
observatory and deep exposures reaching a signal-to-noise ratio of about 1000
per quasar image. This data quality allows us to catch small photometric
variations (a few mmag rms) of the quasar, acting on temporal scales much
shorter than microlensing, hence making the time delay measurement very robust
against microlensing. In only 7 months we measure very accurately one of the
time delays in DES J0408-5354: Dt(AB) = -112.1 +- 2.1 days (1.8%) using only
the MPIA 2.2m data. In combination with data taken with the 1.2m Euler Swiss
telescope, we also measure two delays involving the D component of the system
Dt(AD) = -155.5 +- 12.8 days (8.2%) and Dt(BD) = -42.4 +- 17.6 days (41%),
where all the error bars include systematics. Turning these time delays into
cosmological constraints will require deep HST imaging or ground-based Adaptive
Optics (AO), and information on the velocity field of the lensing galaxy.
