Yb4As3 has an extremely low carrier concentration, which is estimated to be 0.1% per Yb ion, from Hall coefficient and optical reflectivity measurements. The gamma value for Yb4As3 has a value as large as 200 mJ/mole K2 per Yb3+ ion. This gamma value, the extrapolated magnetic susceptibility at 0 K, and the coefficient of T2 in the temperature dependence of the resistivity nearly satisfy the universal relations expected for the heavy fermions. It is hard to understand all these physical properties using a simple extension of the impurity Kondo conception. It is widely believed that Kondo or heavy-fermion systems require a lot of carriers to compensate the magnetic moment. The question is whether it is possible to have a heavy-fermion system with such a low carrier concentration. In order to try and answer this question, we measured the specific heat as a function of temperature, lowering it to 1.5 K, for magnetic fields up to 10 T. It was observed that the linear relation between C/T and T2 was broken by the magnetic field, and that a hump in the specific heat appeared at about 3 T. The position of this hump is shifted to higher T when the field is increased. The total entropy seems to be field independent at high temperatures.