In a distributed system, local access is much faster than remote access. As a help to programmers, some languages require every access to be local. A program in those languages can access remote data via first a shift of the place of computation and then a local access. To enforce this discipline, researchers have presented type systems that determine whether every access is local and every place shift is appropriate. However, those type systems fall short of handling a common programming pattern that we call place-oblivious objects. Such objects safely access other objects without knowledge of their place. In response, we present the first type system for place-oblivious objects along with an efficient inference algorithm and a proof that inference is P-complete. Our example language extends the Abadi-Cardelli object calculus with place shift and existential types, and our implementation has inferred types for some microbenchmarks.