  The detection of the very early gamma-emission of a Type Ia supernova (SNIa)
could provide a deep insight on the explosion mechanism and nature of the
progenitor. However this has not been yet possible as a consequence of the
expected low luminosity and the distance at which all the events have occurred
up to now. A SNIa occurring in our Galaxy could provide a unique opportunity to
perform such measurement. The problem is that the optical flux would probably
be so attenuated by interstellar extinction that would prevent triggering the
observations with gamma-spectrometers at the due time. In this paper we analyse
the possibility of using the anticoincidence system (ACS) of the spectrometer
SPI on board of the INTEGRAL space observatory for detecting the early
gamma-ray emission of a SNIa as a function of the explosion model and distance
as well as of pointing direction. Our results suggest that such detection is
possible at about 6 - 12 days after the explosion and, at the same time, we can
discard missing any hidden explosion during the lifetime of INTEGRAL.
