Hmm, I really don't get it. I just took out the chain, rinsed it off, relubed it and tried again, and the clicking noise is unchanged. I suspect it doesn't have anything to do with the chain after all
I also took out the cassette, gave it a good clean and then put it on with some grease but that also didn't do a thing. Also the sliding rear drop-out is absolutely bomb proof tight and I let it be without trying to tinker with it. Any other ideas of what I could try?