  We report the results from a Chandra TOO observation of the low-luminosity
Narrow Line Seyfert 1 galaxy NGC 4051, obtained during a 6-week duration
low-flux state in 2001 February. During the Chandra observation, the 2-10 keV
source flux was 7e-12 erg/cm^2/s, corresponding to a 2-10 keV luminosity of
8e40 erg/s. We confirm the absence of strong extended soft X-ray emission in
NGC 4051, and that the low state spectrum is dominated by the central point
source. The X-ray spectrum has an unusual, hybrid shape, very soft below ~3 keV
(and which we model with a black body of temperature 0.14 keV) and very hard at
higher energies (power-law slope of Gamma~1). The lightcurves in both soft and
hard bands are significantly variable and correlated, implying a connection
between hard and soft components and proving that the hard component is
dominated by primary continuum emission and is not due to pure reflection from
distant cold material. However, a comparison with RXTE data obtained during the
same 2001 low state suggests the presence of unusually prominent disk
reflection features, which may help to explain the apparent upwards curvature
and extreme hardness of the Chandra spectrum above a few keV. The shape of the
2001 low state spectrum is consistent with that observed in a brief (<3 d) low
flux excursion during the source's normal state in April 2000, suggesting that
emission processes during the low state are not significantly different to
those in the normal state. The unusual spectral shape observed in the low state
may be a continuation to low fluxes of the normal, flux-dependent spectral
variability of the source.
