There is already an existing test (encrypted-media-session-multiple-close.html) that calls close() multiple times, but does so as:
  return Promise.all([mediaKeySession.close(), mediaKeySession.close(), mediaKeySession.close()]);
There doesn't appear to be a test that calls them sequentially.

I changed the code in the repro to end with:
    .then(() => { var p = session.close(); console.log(p); return p; })
    .then(() => { var p = session.close(); console.log(p); return p; })
    .then(() => { var p = session.close(); console.log(p); return p; });
In the console I see:
   Promise {[[PromiseStatus]]: "pending", [[PromiseValue]]: undefined}
   undefined
   undefined
So it acts like a resolved promise, even if it doesn't look like one. 

The code in MediaKeySession.cpp, if the session is already closed, simply uses ScriptPromise::cast() to create a resolved promise:
    return ScriptPromise::cast(scriptState, ScriptValue());
I changed it to create and resolve one of the EME promise wrappers directly:
    SimpleResultPromise* result = new SimpleResultPromise(scriptState, this);
    ScriptPromise promise = result->promise();
    result->complete();
    return promise;
Running that I now see:
    Promise {[[PromiseStatus]]: "pending", [[PromiseValue]]: undefined}
    Promise {[[PromiseStatus]]: "resolved", [[PromiseValue]]: undefined}
    Promise {[[PromiseStatus]]: "resolved", [[PromiseValue]]: undefined}

yhirano, haraken: Should ScriptPromise::cast() not return an object that looks like a promise?

(Note: running the repro on ToT requires the second parameter to requestMediaKeySystemAccess() to be "[{audioCapabilities: [{contentType: 'audio/webm; codecs=vorbis'}]}]", as otherwise it fails with "None of the requested configurations were supported.")

Please don't pass an empty ScriptValue to ScriptPromise::cast. You can use ScriptPromise::castUndefined.

yhirano: Thanks. That fixes it.

The following revision refers to this bug:
  https://chromium.googlesource.com/chromium/src.git/+/665c048b2e508b5cc566810816a77bfd4bfdb9db

commit 665c048b2e508b5cc566810816a77bfd4bfdb9db
Author: jrummell <jrummell@chromium.org>
Date: Sat Feb 11 00:25:25 2017

EME: close() should return a resolved promise if session already closed

BUG= 690664 
TEST=new test passes

Review-Url: https://codereview.chromium.org/2688263002
Cr-Commit-Position: refs/heads/master@{#449804}

[add] https://crrev.com/665c048b2e508b5cc566810816a77bfd4bfdb9db/third_party/WebKit/LayoutTests/media/encrypted-media/encrypted-media-session-multiple-close-sequential.html
[modify] https://crrev.com/665c048b2e508b5cc566810816a77bfd4bfdb9db/third_party/WebKit/Source/modules/encryptedmedia/MediaKeySession.cpp