  We present a search for 183 GHz H_2O(3_13-2_20) emission in the
infrared-luminous quasar MG 0751+2716 with the NRAO Very Large Array (VLA). At
z=3.200+/-0.001, this water emission feature is redshifted to 43.6 GHz. As
opposed to the faint rotational transitions of HCN (the standard high-density
tracer at high-z), H_2O(3_13-2_20) is observed with high maser amplification
factors in Galactic star-forming regions. It therefore holds the potential to
trace high-density star-forming regions in the distant universe. If indeed all
star-forming regions in massively star-forming galaxies at z>3 have similar
physical properties as e.g. the Orion or W49N molecular cloud cores, the flux
ratio between the maser-amplified H_2O(3_13-2_20) and the thermally excited
CO(1-0) transitions may be as high as factor of 20 (but has to be corrected by
their relative filling factor). MG 0751+2716 is a strong CO(4-3) emitter, and
therefore one of the most suitable targets to search for H_2O(3_13-2_20) at
cosmological redshifts. Our search resulted in an upper limit in line
luminosity of L'(H_2O) < 0.6 x 10^9 K km/s pc^2. Assuming a brightness
temperature of T_b(H_2O) ~= 500 K for the maser emission and CO properties from
the literature, this translates to a H_2O(3_13-2_20)/CO(4-3) area filling
factor of less than 1%. However, this limit is not valid if the H_2O(3_13-2_20)
maser emission is quenched, i.e. if the line is only thermally excited. We
conclude that, if our results were to hold for other high-z sources, H_2O does
not appear to be a more luminous alternative to HCN to detect high-density gas
in star-forming environments at high redshift.
