The accelerating expansion of the universe is one of the  
key scientific questions of our day. While other cosmological studies
(CMB, cluster counts) have provided complementary measurements, the Supernova 
(SN) Ia Hubble diagram remains the only direct approach currently in use
to study acceleration.  There are ongoing studies of the details
of all known relevant sources of systematic uncertainty, but none show
any biases at a level that might affect the basic acceleration
results.  It is now time to pursue the cause of
the acceleration --- the ``dark energy'' --- be it a simple ``energy of the
vacuum"  (Einstein's cosmological constant (Lambda) ) or a general
dynamical scalar field.  This proposal is aimed at the
first key step --- testing Lambda.  By adding strategic HST
observations for a sample of SNe Ia from a new, ambitious multi-year
ground-based SN project, it will be possible to dramatically improve
the efficacy of these next-generation SN Hubble diagrams for testing
Lambda. We here propose a highly efficient use of NICMOS
--- based on two complementary techniques --- to achieve this goal by the 
study of 30 z~0.5 SNe Ia, and
thereby provide the crucial improvement in control of systematic
uncertainties necessary to match the statistical uncertainty of which
ground-based searches are capable.