  We present the discovery and extensive early-time observations of the Type Ic
supernova (SN) PTF12gzk. Our finely sampled light curves show a rise of 0.8mag
within 2.5hr. Power-law fits [f(t)\sim(t-t_0)^n] to these data constrain the
explosion date to within one day. We cannot rule out the expected quadratic
fireball model, but higher values of n are possible as well for larger areas in
the fit parameter space. Our bolometric light curve and a dense spectral
sequence are used to estimate the physical parameters of the exploding star and
of the explosion. We show that the photometric evolution of PTF12gzk is slower
than that of most SNe Ic, and its high ejecta velocities (~30,000km/s four days
after explosion) are closer to the observed velocities of broad-lined SNe Ic
associated with gamma-ray bursts (GRBs) than to the observed velocities in
normal Type Ic SNe. The high velocities are sustained through the SN early
evolution, and are similar to those of GRB-SNe when the SN reach peak
magnitude. By comparison with the spectroscopically similar SN 2004aw, we
suggest that the observed properties of PTF12gzk indicate an initial progenitor
mass of 25-35 solar mass and a large (5-10E51 erg) kinetic energy, close to the
regime of GRB-SN properties. The host-galaxy characteristics are consistent
with GRB-SN hosts, and not with normal SN Ic hosts as well, yet this SN does
not show the broad lines over extended periods of time that are typical of
broad-line Type Ic SNe.
