A chip resistor device includes: a dielectric substrate that has top and bottom surfaces and two opposite edge faces interconnecting the top and bottom surfaces; two electrodes that are formed on two opposite sides of the dielectric substrate and that cover the edge faces and parts of the top and bottom surfaces; a resistor layer that is formed on one of the top and bottom surfaces of the dielectric substrate between the electrodes and that is brought into contact with the electrodes; and a heat conductive layer that is disposed on the resistor layer oppositely of the dielectric substrate and between the electrodes, that contacts the resistor layer and the two electrodes, and that has a higher resistance than that of the resistor layer. A method for making the chip resistor device is also disclosed.