Electron microscopy experiments reveal that in a Cu-rich polycrystalline La
2CuO4.003 , grains may phase separate into hole-rich and hole-poor grains a
t room temperature and in a hole-rich crystalline grain, holes are distribu
ted inhomogeneously over a distance that is smaller than 500 nm. In a hole-
rich grain it is shown that hole modulation superlattice reflections may be
induced by electron beam, and the size of the modulation domain is estimat
ed to be around 150 nm. The observed modulation superlattice reflections ar
e shown to result from hole localization around a set of parallel modulatio
n planes that are inclined to the CuO2 planes. When intersecting with a CuO
2 plane, holes lying on and close to the set of modulation planes form a tw
o-dimensional hole stripe pattern on the CuO2 plane. It is suggested that t
he observed static hole stripes result from the pinning of fluctuating stri
pes by electron-beam induced effects. Our results indicate that holes assoc
iated with the same modulation plane but different CuO2 planes are strongly
correlated and interlayer hole interaction is not in general negligible.