We present results of a search for W+W- production through the leptoni
c decay channel W+W- --> l(+)l(-)<v(v)over bar> in <(p)over bar p> col
lision at root s = 1.8 TeV. In a 108 pb(-1) data sample recorded with
the Collider Detector at Fermilab, five W+W- candidates are found with
an expected standard model background of 1.2 +/- 0.3 events. The W+W-
production cross section is measured to be sigma(<(p)over bar p> -->
W+W-) = 10.2(-5.1)(+6.3)(stat) +/- 1.6(syst) pb, in agreement with the
standard model prediction. Limits on WW gamma and WWZ anomalous coupl
ings are presented.