  We report on an observation of the recently discovered accreting millisecond
X-ray pulsar IGR J00291+5934 performed with the RXTE-Proportional Counter Array
(PCA) and Chandra-High Energy Transmission Grating Spectrometer (HETGS). The
RXTE data are from a two week follow-up of the source while the Chandra
observation took place around the end of the follow-up, about 12 days after the
discovery of the source, when the source flux had decreased already by a factor
of ten. The analysis of the Chandra data allowed us to extract the most precise
X-ray position of IGR J00291+5934, RA=00 29 03.08 and Dec=+59 34 19.2 (0.6sec
error), compatible with the optical and radio ones. We find that the spectra of
IGR J00291+5934 can be described by a combination of a thermal component and a
power-law. Along the outburst detected by PCA, the power-law photon index shows
no particular trend while the thermal component (~1 keV, interpreted as a hot
spot on the neutron star surface) becomes weaker until non-detection. In the
simultaneous observation of the weak Chandra/RXTE spectrum, there is no more
indication for the ~1 keV thermal component while we detect a colder thermal
component (~0.4 keV) that we interpret as the emission from the cold disc. A
hint for a 6.4 keV iron line is detected, together with an excess around 6.8
keV and absorption feature around 7.1 keV. The latter two features have never
been detected in the spectra of accretion-driven millisecond pulsars before
and, if confirmed, would suggest the presence of an expanding hot corona with
high outflow velocities.
