  The star S2 orbiting the compact radio source Sgr A* is a precision probe of
the gravitational field around the closest massive black hole (candidate). Over
the last 2.7 decades we have monitored the star's radial velocity and motion on
the sky, mainly with the SINFONI and NACO adaptive optics (AO) instruments on
the ESO VLT, and since 2017, with the four-telescope interferometric beam
combiner instrument GRAVITY. In this paper we report the first detection of the
General Relativity (GR) Schwarzschild Precession (SP) in S2's orbit. Owing to
its highly elliptical orbit (e = 0.88), S2's SP is mainly a kink between the
pre-and post-pericentre directions of motion ~ +- 1 year around pericentre
passage, relative to the corresponding Kepler orbit. The superb 2017-2019
astrometry of GRAVITY defines the pericentre passage and outgoing direction.
The incoming direction is anchored by 118 NACO-AO measurements of S2's position
in the infrared reference frame, with an additional 75 direct measurements of
the S2-Sgr A* separation during bright states ('flares') of Sgr A*. Our
14-parameter model fits for the distance, central mass, the position and motion
of the reference frame of the AO astrometry relative to the mass, the six
parameters of the orbit, as well as a dimensionless parameter f_SP for the SP
(f_SP = 0 for Newton and 1 for GR). From data up to the end of 2019 we robustly
detect the SP of S2, del phi = 12' per orbital period. From posterior fitting
and MCMC Bayesian analysis with different weighting schemes and bootstrapping
we find f_SP = 1.10 +- 0.19. The S2 data are fully consistent with GR. Any
extended mass inside S2's orbit cannot exceed ~ 0.1% of the central mass. Any
compact third mass inside the central arcsecond must be less than about 1000
M_sun.
