  We find the space-time supersymmetric and kappa-invariant action for a
D3-brane propagating in the AdS_5 x S^5 background. As in the previous
construction of the fundamental string action in this maximally supersymmetric
string vacuum the starting point is the corresponding superalgebra su(2,2|4).
We comment on the super Yang-Mills interpretation of the gauge-fixed form of
the action.
