We present near-infrared (NIR) time-series spectroscopy, as well as complementary ultraviolet (UV), optical, and NIR data, of the Type Ia supernova (SN Ia) iPTF13ebh, which was discovered within two days from the estimated time of explosion. The first NIR spectrum was taken merely 2.3 days after explosion and may be the earliest NIR spectrum yet obtained of a SN Ia. The most striking features in the spectrum are several NIR CI lines, and the CI {lambda}1.0693um line is the strongest ever observed in a SN Ia. Interestingly, no strong optical CII counterparts were found, even though the optical spectroscopic time series began early and is densely-cadenced. Except at the very early epochs, within a few days from the time of explosion, we show that the strong NIR CI compared to the weaker optical CII appears to be general in SNe Ia. iPTF13ebh is a fast decliner with {Delta}m15(B)=1.79+/-0.01, and its absolute magnitude obeys the linear part of the width-luminosity relation. It is therefore categorized as a "transitional" event, on the fast-declining end of normal SNe Ia as opposed to subluminous/91bg-like objects. iPTF13ebh shows NIR spectroscopic properties that are distinct from both the normal and subluminous/91bg-like classes, bridging the observed characteristics of the two classes. These NIR observations suggest composition and density of the inner core similar to that of 91bg-like events, and a deep reaching carbon burning layer not observed in slower declining SNe Ia. There is also a substantial difference between the explosion times inferred from the early-time light curve and the velocity evolution of the SiII {lambda}0.6355um line, implying a long dark phase of ~4 days.