We report precise measurements of the DO and D+ meson lifetimes by the
E687 Collaboration at Fermilab. The measurements have been made using
16000 fully reconstructed decays of the D0 into the K-pi+ and K-pi+pi
-pi+ final states and 9000 decays of the D+ into the K-pi+pi+ final st
ate. The lifetimes of the D0 and D+ mesons are measured to be 0.413+/-
0.004+/-0.003 ps and 1.048+/-0.015+/-0.011 ps respectively.