  We show that the reduced Khovanov homology of an oriented link $L$ in $S^3$
can be expressed as the homology of a chain complex constructed from a
description of $L$ as the closure of a 1-tangle diagram $T$ in the annulus. Our
chain complex is constructed using a cube of resolutions of $T$ in a manner
similar to ordinary Khovanov homology, but it is typically smaller than the
ordinary Khovanov chain complex and has several unusual features, such as long
differentials corresponding to pairs of successive saddles in the cube of
resolutions. Our chain complex carries a natural filtration, which we use to
construct a spectral sequence that converges to reduced Khovanov homology. Our
results are part of a larger program to construct an analog of Khovanov
homology for links in lens spaces by generalizing a symplectic interpretation
of Khovanov homology due to Hedden, Herald, Hogancamp, and Kirk, and our chain
complex was predicted by this program for the case when the lens space is
$S^3$.
