I don’t find it in my 14th Chicago, so maybe it comes from Words into Type but, I would go with end of the line so you don’t have the distracting space at the left side.

This may just be style rather than a rule.

I would never place an em dash (or any other type of dash) at the beginning of a new line, and I’ve heard the same opinion from other people at different places where I’ve worked.

Since in many ways a dash functions like a parenthesis, to signal a thought related to, but not essential to the main sentence, does this mean that you also would not start a line with a parenthetical comment?

The way we use to handle this with TeX was to put in a whopping penalty for breaking a line immediately before a dash, and a small penalty for breaking after the dash — as you may know, TeX uses a paragraph optimization routine which is programmable. So, if a line broke before the dash — it started a new line — we were pretty sure that any other decision would involve a huge compromise.

To James: if making a line is the only way out of your pagination problem, and that’s the only place you can make a line, go ahead & break after the dash.

Which isn’t to say somebody won’t criticize it. One of my favorite stories was where an editor marked our proof “P.E. — hyphenated last word,” and “P.E. — loose line.” I assure you, the last word in the paragraph we hyphenated was quite long; over six letters went down. Now, did the editor think that line above was going to set any tighter if we took down more letters (didn’t hyphenate)? Oh, and did I mention there were only two lines in that paragraph?

What we wound up doing was to take down the entire word, which meant using about an em-space between words in that first line. We also disallowed the PE, & made them take is as an Editor’s Alteration.

The dash might follow along with hyphenation break rules where the parenthesis might follow the exception as quotation marks. You’ve got to have some room for common sense (whatever that is) because multi-column narrow measure editorial won’t ever work like a nice single column book page.

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Since in many ways a dash functions like a parenthesis, to signal a thought related to, but not essential to the main sentence, does this mean that you also would not start a line with a parenthetical comment

Dashes don’t always come in pairs, the way parentheses do.

I like Bruce’s explanation in the thread Florian has linked to:

I have always gone by the notion that written words are a way of capturing speech and making it live again in the brain of the reader. If the dash is supposed to convey a sense of pause, then it seems to me to be more effective at the end of the first line. This way the reader encounters the pause indicator, then takes a brief moment to move back over to the next line, and the elapsed time is slightly longer. Encountering it at the beginning of the next line comes as more of a surprise. Therefore, in my style book the dash is always best located at the end of the first line, but if spacing conditions make that ungraceful or impratical, then it goes at the beginning of the next line. The tiniest of subtleties, this, but fun to think about!

Quite articulate, that Bruce.

In Finnish there’s a lot of hyphens, so common style is to move dash to the next line to avoid confusion. Especially when there are plenty of people who use hyphen instead of dash.

Yes, there are two functions for dashes (many marks have more than one function, for instance the apostrophe and single right quote are the same character).

So, if the dash is part of a pair of dashes, used similarly to parentheses or commas, then don’t put it at the beginning of a line, but if it is single “lead-in”, then you may.

I have many opinions — though I am often wrong.

I have many opinions (though I am often wrong).

Using parentheses means perforce that you use 2. You use two dashes only when the sentence continues after the “parenthetical” remark.

The usual “rule” against beginning a line with a dash is not a grammatical one, but typographic: the dash seems to weaken the text edge. What is so often forgotten is that line-breaking almost always involves a series of typographic compromises. If you want to use em-spaces to justify a line in order to avoid beginning a line with a dash, that’s your business. Just remember that ironclad rules also have consequences.

This is one reason to use shorter (perhaps 3/4) em dashes flanked with some amount of space. In the middle of a measure, it might ultimately occupy the same length as an unspaced, full em dash, but when it falls at the end of a line, the right flanking space can be removed, giving you a shorter irreducible unit. Might not help much, but it’s something.