Hi Rick,
I've not saved Swiss Chard seeds since I've never gotten it to over winter. But I am a big proponent of leaving the plant and seeds intact on any plant until the seed is ready to harvest so cutting them off in my opinion is not a good idea and you will lose viability. I just checked my Seed to Seed book and it says that the whole plants can be pulled when the seeds are fully mature to finish drying in a like a garage or whatever.
Remy

I can't help you with the 'correct' answer. But in my climate chard always overwinters and always self sows. I tend to pull the plants before the seed is dry because it takes a VERY long time to ripen. I then put the plants on the (cold)compost heap. I subsequently spread the compost and get a new crop of chard without any effort. So from this, completely unscientific, experience I would say that chard will grow from seed which is not fully ripened on the plant. This seems to agree with remy's advice.

Thanks for the replies, Remy and Flora. I managed to talk Laura out of making me remove the chard plants (by removing the seed stock of Red Kale and Spinach to make lots of room,) so they're still in the garden, and the seeds appear to be getting near mature and starting to turn brownish. I will probably harvest them in the next week or so, and dry them out in the sun. Wish I would see some volunteers to let me know they're viable, but they seem to hold on to their seeds pretty strongly.

I have some I am going do an experiment pulling and allowing to ripen on a tarp. I just like to experiment for my amusement.

Also, you can keep swiss chard alive for up to or over 3 years simply by removing the seed stalks. it won't produce as well, but if it is an ornamental, it could be worth saving for you. Esp. if you don't have the time or energy to replace it just yet.