We present an ultrafast transient absorption spectroscopy system in the visible combining high-sensitivity broadband detection with extreme temporal resolution. The instrument is based on an ultrabroadband sub-10 fs optical parametric amplifier coupled to an optical multichannel analyzer with fast electronics, enabling single-shot detection at 1 kHz repetition rate. For a given pump-probe delay tau, we achieve a differential transmission (DeltaTT) sensitivity of the order of 10(-4) over the lambda(pr)=490-720 nm probe wavelength range by averaging over 1000 shots, allowing the acquisition of complete two-dimensional DeltaTT (lambda(pr),Tau) maps within a few minute measurement time. We present application examples highlighting the capability of this instrument to observe ultrafast dynamical processes, follow impulsively excited vibrational motions with frequency as high as 3000 cm(-1) (11 fs period), and determine the probe wavelength dependence of amplitude and phase of the oscillations.