(This is a Rupert Sheldrake experiment from 2002. The first unusual thing about N’kisi the parrot is that he had a vocabulary of 1200 words and spoke in grammatically constructed phrases, using combinations he had never heard before. The second is that he was psychic.)
Aimée Morgana noticed that her language-using African Grey parrot, N’kisi, often responded to her thoughts and intentions in a seemingly telepathic manner. We set up a series of trials to test whether this apparent telepathic ability would be expressed in formal tests in which Aimée and the parrot were in different rooms, on different floors, under conditions in which the parrot could receive no sensory information from Aimée or from anyone else. N’kisi’s “task” was to talk about a picture selected at random from a sealed envelope and presented to Aimée in a distant room.

During these trials Aimée and the parrot were both videotaped continuously. We conducted a total of 149 two-minute trials. He scored 23 hits, when the expected number by chance was 12. The probabiliy that this could have occurred by chance was 0.00025.
Read more details or Read an academic write-up of the experiment or a BBC News story