Hearthpwn

Imo this has potential to be played in constructed, it's not so bad, as people think it is.

Explanation: Now many people may disagree and won't take it serious, but imo this card can find a home in zoolock or maybe in disco, when you need to throw  an useless card away. It's another thing whether or not zoo and disco desperately need that card, but who knows.
The reason for this is - a not so great statted minion, that however gives you a spell. And that's important to mention, because in those type of decks people don't run spells at all (almost; with the exception of Soulfire and Forbidden ritual). So this card counts as two - a body + a "free" spell. And I purposely call it free, because these type of decks don't really care about healing or dropping that low on health. You don't care about the late game - you need to rush down your opponent as much as possible. There are spells, that you will find useful, if you discover them: Bloodfury Potion, Soulfire, another Forbidden Ritual, Mortal Coil, Shadow Bolt - also a good option, maybe Kara Kazham! and Feeding Time, you can even find a removal, if you are desperate to remove a big taunt or so. In wild there are even more and better options. Since with the hero power you are "diggin" for answers, this card will come in handy.

Note: Because there aren't any good healing options in standard, this card will be risky in the handlock deck. The health price will be too much to pay and it won't be worth it + why run a risky card, than can damage you and end the game in favour for your opponent, when you can include the spells instead.

@RyeDoge

In standard or wild?

It's more easy to explain in wild - Antique Healbot, Refreshment Vendor - these cards heal for bunch and synergize well with brann. If you are a fan if reno, then he is an option too. The healing is really significant in order to sustain your hero. Because the taunts only block future physical damage (aka minion's or weapon damage).

In standard you can heal with Earthen Ring Farseer and Mistress of Mixtures - those are the best options. The other healing neutral minions are either not worth it to include Gadgetzan Socialite for an example, or super conditional, like Cult Apothecary. If you run Kabal Courier, you have a chance to discover a priest healing card, but it depends on RNG.

So if I could make a good neutral healing card, that would be used by warlocks and other non heal classes, it would definitely  be a version of Jinyu Waterspeaker. 

If this is not what you were asking, then please reexplain your question.

Note: Although there are better healing options in wild, I would still not recommend using Chittering Tunneler in anything but disco/zoo. Handlock doesn't need a card, that will damage himself, because that deck normally uses expensive ones (removals are relatively costly) and the bigger the cost, the bigger the damage from Tunneler + you have to pay the price of casting it too. And also why would you include a card, that won't always give you the needed answer, it's better to include the spells themselves, rather than an additional minion.
But the card isn't bad on its own - I tested it in arena and the results were pleasing. In the games, where I rushed down my opponent, the Tunneler came in handy.

Quote from UmtheMuse >>

Also wanted to point out that Violet Illusionist and Lord Jaraxxus can be used to mitigate the damage.

This card is terrible when you're fishing for answers. Instead, play it to proactively get some low-cost answers.

that's why only fast decks should use it, because they don't run that much spells and this card can give them something they need - either burst, removal, minions etc.
control lock doesn't need to gamble, they will lose if they rely on the RNG

Quote from UmtheMuse >>

Huh? You're the one who made the case for Chittering Tunneler plus a heal card. I was just chiming in with more options. The nice thing about these two is that you can afford to reach for a more expensive spell. Fast decks can't afford to put in things like Siphon Soul or Bane of Doom, but you'd be happy to pick one up if you happen to have the Tunneler and Illusionist together or if you plan to use the Lord Jaraxxus on your next turn. Of course, this wouldn't happen in a zoo deck, but maybe a mid-range deck could get away with them.

play it to proactively get some low-cost answers.

Let's look at the cheap spells. Soulfire may help you with clearing a minion really cheap, but it will discard you a card. And if this card is a removal or a taunt, they you will have a bad time as a control lock. The other cheap spells, a control lock can use, are Mortal Coil, Shadow Bolt, Corrupting Mist and Drain Life maybe. In wild you have Power Overwhelming as well. BUT if you look at the other cheap cards, then you will see, that mainly zoo and disco zoo benefit from them -  Forbidden Ritual, Bloodfury Potion, Demonfire, Sense Demons, as well as the cheap spells mentioned above. So in conclusion Tunneler is only useful in those type of decks. Control locks and value locks can use Kabal Courier instead.