This ID is very interesting to me and I think needs a lot more testing, and could possibly explode in power if given the right tools. The biggest advantage of this identity is that it terrifies the runner from wanting to run until most of their rig is out. Common knowledge dictates that the way to play around PE type decks is to not run until most of the cards in your hand are tolerable to lose. PE can poke at your by scoring a few things themselves, but the damage is random and PE tends to run a lot of easy-to-score 1 point agendas to shave you as much as possible. The only big agenda they tend to use is #the future perfect, so when they try to score it early you can usually wager if the damage risk is worth 3 points, which it usually is. This means that handing some early tempo to PE so you can safely set up is annoying, but usually not that bad, since they might get 1 or 2 points/damage.
Chrono Trigger here ramps that initial pressure up immensely, and when used correctly, this ID should theoretically almost guarantee you an early game lead. Almost all the cards that proc the ID can only be used if the runner runs (Neural EMP, ice, Shock!. And since even 1 or 2 damage early on means the runner WILL lose the most valuable cards in their hand and lose a buttload of tempo, the smart runner will (and should) essentially concede the early game to the corp so that they can set up their rig/econ in peace. In PE, this means getting 1 or 2 points. In a Chrono deck with some good rush potential, this could mean the corp getting 3-4 agenda points and setting up their own economy practically uncontested. I shouldn't have to tell you that being halfway to victory before the runner even starts running is a big, fat, sweaty advantage so infuriating and pressure-heavy it might as well be a Yolo t-shirt in a vice.
However, like all damage decks, it only hits the hand, and like most rush decks, it falls off late game when your gear checks don't work anymore. What this ID needs is the ability to trash programs regularly and set the runner back to square one. While there are several cards that attack the runners rig, I think 2 cards in particular in the new set are going to work very well in Chrono. The upcoming Salem's Hospitality, and the new Kala Ghoda Real TV. Hear me out on this:
Salem - Enables you to trash the cards you want WITHOUT the runner having to run. This shuts off part of the counterplay to the the ID. Land even one damage, and you know what to name for salem, essentially doubling your Chrono procs. Proper meta knowledge and game skill also make this card terrifying in the hands of an expert. Also, I can't help but think of all the times you could use it turn one and just name Sure Gamble. The look on the runner's face....
Kala TV - While most people glossed over this card as a "good but not good enough" type of card, I think it has some real synergy with Chronos and Salem. By dropping this early, you know almost everything the runner is drawing, meaning you know what to name for salem, thereby getting chrono procs without doing damage at all. Plus, while ChroPro has massive control over your hand and you can add trash effects to gain (possible) control over the field, Kala TV extends your control to a new area: their deck. By smacking what the runner wants out of their hand, being able to trash things off their field and making sure they never even GET the vital tempo-reviving draws they need, you are effectively controlling literally every aspect of the runners game. Plus Salem is an alliance card, and 3 J-How plus 3 KTV is 6 influence and makes your 3 Salem witch-hunts TOTALLY INFLUENCE FREE.
Again, this is all theoretical, but I find it hard to deny the potential power of this deck. In the hands of an experienced player, this shell could be the single most gut-wrenchingly scary ID to face in the game. The soul-crushing surgical dissection of your deck and demoralization of never having what you want, never keeping what you want and never getting what you want, this could be one of those decks that loses you friends.
EDIT: OMFG ADD HOUSEKEEPING. With one dropped early game, the runner can't run because they'll lose cards and they can't set up because they'll lose cards. The rock-and-a-hard place senario there is...just....wow......