We have measured the low-temperature specific heat C(T) for polycrystalline MgB(2) prepared by high pressure synthesis. C(T) below 10 K vanishes exponentially, which unambiguously indicates a fully opened superconducting energy gap. However, this gap is found to be too small to account for T(c) of MgB(2). Together with the small specific heat jump Delta C/gamma(n)T(c) = 1.09, scenarios such as anisotropic s-wave or multicomponent order parameter are called for. The magnetic field dependence of gamma(H) is neither linear for a fully gapped s-wave superconductor nor H(1/2) for nodal order parameter. It seems that this intriguing behavior of gamma(H) is associated with the intrinsic electronic properties other than flux pinning.