In this paper the problem of error detection in elliptic curve point multiplication is faced. Elliptic Curve Point Multiplication is often used to design cryptographic algorithms that use fewer bits than other methods with the same security level. One of the mode used to break the security of cryptosystem is the injection of a fault in the hardware realizing the cryptographic algorithm. Therefore, to avoid this kind of attack, is very important to develop cryptosystems that are able to detect errors induced by a fault. The paper takes into account the algorithm for elliptic Curve Point Multiplication based on a sequence of additions called “addition chain” and shows how suitable modifications of the algorithms used for computing the point multiplication adds the error detection property to the algorithm.