We present a phase field model of solidification which includes the effects of the crystalline orientation in the solid phase. This model describes grain boundaries as well as solid-liquid boundaries within a unified framework. With an appropriate choice of coupling of the phase field variable to the gradient of the crystalline orientation variable in the free energy, we find that high angle boundaries undergo a premelting transition. As the melting temperature is approached from below, low angle grain boundaries remain narrow. The width of the liquid layer at high angle grain boundaries diverges logarithmically.