HTTP response code for POST when resource already exists

I'm building a server that allows clients to store objects. Those objects are fully constructed client-side, complete with object IDs that are permanent for the whole lifetime of the object.

I have defined the API so that clients can create or modify objects using PUT:

PUT /objects/{id} HTTP/1.1...{json representation of the object}

The {id} is the object ID (defined by the client), so it is part of the Request-URI.

Now, I'm also considering allowing clients to create the object using POST:

POST /objects/ HTTP/1.1...{json representation of the object, including ID}

Since POST is meant as "append" operation, I'm not sure what to do in case the object is already there. Should I treat the request as modification request or should I return some error code (which)?