Early observations of Type Ia supernovae (SNe Ia) provide a unique probe of their progenitor systems and explosion physics. Here we report the intermediate Palomar Transient Factory (iPTF) discovery of an extraordinarily young SN Ia, iPTF 16abc. By fitting a power law to our early light curve, we infer that first light for the SN, that is, when the SN could have first been detected by our survey, occurred only 0.15-0.07+0.15 days before our first detection. In the ∼24 hr after discovery, iPTF 16abc rose by ∼2mag, featuring a near-linear rise in flux for ∼3 days. Early spectra show strong C II absorption, which disappears after ∼7 days. Unlike the extensively observed Type Ia SN 2011fe, the (B - V)0 colors of iPTF 16abc are blue and nearly constant in the days after explosion. We show that our early observations of iPTF 16abc cannot be explained by either SN shock breakout and the associated, subsequent cooling or the SN ejecta colliding with a stellar companion. Instead, we argue that the early characteristics of iPTF 16abc, including (i) the rapid, near-linear rise, (ii) the nonevolving blue colors, and (iii) the strong C II absorption, are the result of either ejecta interaction with nearby, unbound material or vigorous mixing of radioactive 56Ni in the SN ejecta, or a combination of the two. In the next few years, dozens of very young normal SNe Ia will be discovered, and observations similar to those presented here will constrain the white dwarf explosion mechanism.