Thanks again for the info guys.
I'm not a logger, just a guy who likes light weight and high power. I know the saw is only 50.1cc but it makes 3.7bhp which is only .2bhp less than either the Husky 359 or the Stihl MS290; and it's several pounds lighter.
Yes, the chain that came with the saw is a H30 078G (whatever that means). It looks like the part number is 5018406-78.
I see there are also H-25, H-36, H-37-38 and H-80-81 listed on the back of the box. So I should stick with the H30, right? Are either of the other chains mentioned better (Oregon 95VP/Husky H30, or the Carlton 20NK)?
Frosty
Your chain is a .325 pitch
Narrow
Kerf chain, or as Husqvarna refers to it: a Pixel chain. Oregon 95VP is the same chain, it's actually Oregon that manufactures the H30 for Husqvarna. Don't change this unless you go for a shorter bar.
A NK chain is less wide than a traditional .325 pitch chain and since it takes narrower bites in the wood it requires less power from the saw to pull it. They are mostly used on smaller saws that are not that powerfull. An alternative setup is to use NK chains on bars that are at or beyond what the saw actually can handle (here's where you're at).
The reason for the raising of eyebrows is that the 346 is a speed racer for fast cuts in small dimension wood, and if your permanent need was a 20" bar, you should have considered getting a 357. Now, since you use NK chain it'll probably be fine, just not awesome&fantastic.
If you want to change chain you need to match the following:
First: The drive sprocket (spur sprocket or rim) on your clutch drum must match the pitch of your chains, as must the sprocket tip of your bar, unless it is a hard nose that has no nose sprocket. Pitches you might find is 3/8 low profile, .325 and 3/8. There's also 1/4, .404 and 1/2, but they are for special applications, or at least not considered common for chain saws today.
Notice that .325 and .325NK should be considered incompatible even though they might mix - leave for the experienced operator to test - and that 3/8 low profile and 3/8 really are incompatible.
Second: The gauge of your chain must match the gauge on your bar. Common gauges are: .043, .050, .058 and .063. Stihl uses all of them, Husqvarna does not use the smallest. No gauge is better or worse, they are just different because of culture and habits in different areas and countries. Also note that even if all Husqvarna/Oregon NK chains/bars is .050 gauge, not all .050 gauge is NK!
The drive and nose sprockets does not care what gauge you use, change as you please.
Now, if you want 3/8 chain on your 346 you will have to change drive sprocket, bar and of course chain, and I don't think even the most die-hard-long-bar-users will say that 3/8 will work well on a 346 with a 20", so the bar would have to be shorter.