Psionic Animals

Yes, a couple.

The CT A:2 Research Station Gamma has a few and then there is The Traveller Adventure.

Everyone with an interest in the Third Imperium has a duty to read CT Adventures 1-3 and The Traveller Adventure at least once :)
Are there any published examples of animals with psionic abilities?
Yes, there are. Refer to the pseudosaur and the mindwhacker in Referees Briefing: Garden Worlds, and the shakuurzarpi in Core Adventure 1: Invasive Species.

Also, don’t the chamax have some psionic abilities? I seem to remember that being a factor in the first adventure of Pirates of Drinax.
In Mongoose JTAS issue 4, there are three psionic animals. The Psi-bee is an insect analogue that exhibits a psionic hive mind. The next is the Ship's Cat, which has the ability to comfort emotionally distressed crewmembers and [apparently] teleport past locked doors. Lastly, there is also a Zhodani quadruped named a 'ziavbro' that is psionic with a Psi stat of 12 and Awareness and Telepathy Talent 0. They look like a three-eyed purple Samoyed dog.

In MgJTAS 6 there are also two animals that are emote-ivores. While they don't have psionic statistics, I suggest that gaining nourishment via empathy is a psionic ability of some form. They are 'Sac'se'qan' and the 'Khal'oman'. The sac'se'qan feeds off anger and aggressive behavior and the khol'oman feeds off dreams.

He sees you when you're sleepin',
He knows when you're awake,
he knows if you've been bad or good,