Don't be the team's tank for starters. That's my #1 rule. Chen + hard tank (Muradin, Johanna especially). That is what you want.
Most Chen builds - if not all of them - go for the regen/shielding survival talents. Honestly, I just don't get that.
My talent build is:
Bottomless Mug - no idea why this isn't taken more often. It gives you a second cycle of Chen's spells which - because they're on 5s cooldown - amounts to a lot of damage. Without this talent you will be drinking off the cycle, with it you'll be doing the cycle again. It's not a hard choice, IMO, especially when Chen himself is particularly vulnerable to having his drinking interrupted and thus his damage potential literally cut off. The less drinking mid-combat, the better. Hidden bonus: Brewmaster's regen will almost always be up with Bottomless Brew. I consider that a good thing.
Deep Breath - used to be Amplified Healing, but after a few tests in Try Mode I decided the talent wasn't worth the few extra life per second. I'm not there to heal, I'm there to deal damage. Deep Breath was way more effective than I thought it would be. Again, another talent that (per the stats) is almost never taken.
Brewmaster - always.
Storm Spirits - always. Barrel is bugged for starters, and you're better off leaving the CC to champs who can do it better. Storm Spirits are excellent body blockers and can actually trap some of the smaller heroes. The ult also provides you a functional second life bar + huge mobility.
Relentless - always. Gives you the ability to keep going.
Pressure Point - always. Arguably Chen's best talent alongside Brewmaster. People wanted this to be a stun in another Chen thread, but that would be super OP. Chen's Q is on a 5s cooldown. So you hit them with this, wait for the slow to roll off, then hit them with W-E. By the time that slow rolls off, you'll be ready to hit them with another Q. All the while you (and maybe a lightning spirit) are mixing in attacks. Very few can escape this.
Elemental Conduit - always. More damage. Q releases the ranged lightning spirit. Good to know for a lot of reasons, but the best of them is to cycle him into attacking mercenary bosses (Q + W + E, wait, do it again, spawning another lightning; the spirit is up for 4s, which gives you 1s between the cycle of him being gone; not a big deal).
Team fights: wait for tank to roll in, pick your spot, dive in, preferably on a mage or DPS. Sometimes I'll chase a healer (if it's a Rehgar, for example, just to get him off his game/distracted, but I'd never go after a healer like Uther, there's no point). Q in, W + E, and most of the time, watching for the CC, go right into your ult. There's rarely a good reason to not ult. With all the CC flying about, you're better off ulting and doing more damage that way. Obviously, it's up to your discretion.