Specific heat for single crystalline samples of Ce1-xLaxOs4Sb12 at zero-field and magnetic fields to 14 T is reported. Our results confirm enhanced value of the electronic specific heat coefficient in the paramagnetic state. They provide arguments for the intrinsic origin of the 1.1 K anomaly. This transition leads to opening of the gap at the Fermi surface. This low temperature state of CeOs4Sb12 is extremely sensitive to chemical impurities. 2% of La substituted for Ce suppresses the transition and reduces the electronic specific heat coefficient. The magnetic field response of the specific heat is also anomalous.