  The KKLT construction of de Sitter vacua includes an uplifting term coming
from an anti-D3-brane. Here we show how this term can arise via spontaneous
breaking of supersymmetry, based on the emergence of a nilpotent chiral
supermultiplet on the world-volume of the anti-D3-brane. We establish and use
the fact that both the DBI as well as the WZ term, with account of
orientifolding, acquire a form of the Volkov-Akulov action. For an O3
orientifold involution of $\mathbb{R}^{9,1}$ we demonstrate the cancellation
between the fermionic parts of the DBI and WZ term for the D3-brane action. For
the anti-D3-brane we show that the DBI action and the WZ action combine and
lead to the emergence of the goldstino multiplet which is responsible for
spontaneous breaking of supersymmetry. This provides a string theoretic
explanation for the supersymmetric uplifting term in the KKLT effective
supergravity model supplemented by a nilpotent chiral multiplet.
