  There is mounting observational evidence that the expansion of our Universe
is undergoing a late-time acceleration. Among many proposals to describe this
phenomenon, the cosmological constant seems to be the simplest and the most
natural explanation. However, despite its observational successes, such a
possibility exacerbates the well known cosmological constant problem, requiring
a natural explanation for its small, but nonzero, value. In this paper we
consider a cosmological scenario driven by a varying cosmological term, in
which the vacuum energy density decays linearly with the Hubble parameter. We
show that this model is indistinguishable from the standard one in that the
early radiation phase is followed by a long dust-dominated era, and only
recently the varying cosmological term becomes dominant, accelerating the
cosmic expansion. In order to test the viability of this scenario we have used
the most recent type Ia supernova data, i.e., the High-Z SN Search (HZS) Team
and the Supernova Legacy Survey (SNLS) Collaboration data. In particular, for
the SNLS sample we have found the present matter density and Hubble parameters
in the intervals [0.27, 0.37] and [0.68, 0.72], respectively (at 95% c.l.),
which is in good agreement with the currently accepted estimates for these
parameters.
