We present the results of a search for the top quark in 19.3 pb^{-1} of p pbar collisions at sqrt{s}= 1.8 TeV. The data were collected at the Fermilab Tevatron collider using the Collider Detector at Fermilab (CDF). The search includes Standard Model t tbar decays to final states e e nu nubar, e mu nu nubar, and mu mu nu nubar as well as e + nu + jets or mu + nu + jets. In the (e, mu) + nu + jets channel we search for b quarks from t decays via secondary-vertex identification and via semileptonic decays of the b and cascade c quarks. In the dilepton final states we find two events with a background of 0.56^{+0.25}_{-0.13} events. In the e, mu + nu + jets channel with a b identified via a secondary vertex, we find six events with a background of 2.3 +- 0.3. With a b identified via a semileptonic decay, we find seven events with a background of 3.1 +- 0.3. The secondary-vertex and semileptonic decay samples have three events in common. The probability that the observed yield is consistent with the background is estimated to be 0.26%. The statistics are too limited to firmly establish the existence of the top quark, however a natural interpretation of the excess is that it is due to t tbar production. We present several cross checks. Some support this hypothesis, others do not. Under the assumption that the excess yield over background is due to t tbar, constrained fitting on a subset of the events yields a mass of

174 \pm 10^{+ 13}_{- 12} GeV/c^2

for the top quark. The t tbar cross section, using this top quark mass to compute the acceptance, is measured to be 13.9^{+6.1}_{-4.8} pb.

PACS Numbers: 14.80.Dq, 13.85.Qk, 13.85.Ni