A self-applicable partial evaluator for the Lambda calculus of objects is presented in this paper which is an untyped Lambda calculus extended with object primitives. The classic three steps methodology is used to construct the partial evaluator. First, a meta interpreter is defined for the language. Second, an abstract analysis (binding-time analysis) is introduced to determine which operations can be executed at compile time and which operations will be executed at run-time. Finally, the self-applicable partial evaluator is exhibited. Proofs of the correctness of the meta-interpreter and self-applicable partial evaluator are also given in this paper.