How to I safely anchor a safety line to a chimney?

A suitable ladder stabiliser would provide a little extra extra security.

Attaching to the chimney is not a good idea. Just forget about that idea.

If you want to protect against a fall while you are at the top of the chimney, you need to anchor your line at or above your working height. If you don't have anything else near by then you're out of luck.

I recommend looking to to renting a towable manlift.

There is no reliable data I know of for the ultimate strength of expansion anchors in brick masonry. It's not a viable anchor system no matter how many you use (within reason). You are almost better off with no protection because then you will make damn sure you do not fall. (Just kidding, but there is some logic to this amongst rock climbers).

An anchor system around the entire chimney is a much better option if properly placed. As you note, there is a risk of the entire chimney failing. This risk is difficult to assess, depending on the chimney's age, method of construction (reinforced?), type of brick, the mortar mix used, it's anchorage to adjacent structure, etc. The anchor should be placed as close to the highest chimney anchorage as possible, though it increases your fall distance, it decreases the bending moment in the structure.

If the resulting fall distance is unacceptable, or there is no anchorage, you need to consider alternatives. An anchor system installed into the structure of the building is most secure. This allows possibly a higher anchor (less fall distance) and a more desirable fall factor (proportionally more rope involved for a given fall distance reduces shock loading). This will involve locating structural members and using appropriate fasteners, as well as dealing with sealing around the anchor to prevent roof leaks.

There are manufactured fall arrest anchors suitable to such applications. By following recommended installation instructions, these anchors in the US are OSHA approved and will resist 5000 lbs of force. This is the only sure way of achieving an adequate anchor system.

In the US, OSHA fall protection requirements are applicable to work done on single family residences.

That's the official line as I know it. That said, I have a similar situation where I sank a single 5/16"x3" solid, shouldered eye screw (hot dipped galvanized) into the center of one roof rafter, straight through the roofing, sealant applied before applying the final few turns. It's been there for decades with no evidence of leakage or corrosion. It does not meet OSHA standards but I consider it marginally adequate in the event of a fall for my particular situation. It will not be adequate for other situations.

Why not try something like this:

1. set up two anchor points, such as large hookeyes, screwed into the wooden siding on either side of the house in line with the chimney
2. attach a safety line to one hookeye and toss it over the peak if the roof near the chimney
3. attach to the other hookeye leaving some slack.
4. attach your safety line to the transverse line.

You could put knots or loops into the transverse line to create natural stops in the event of a slip.

Or you could call in a pro (I hate high ladders and roof work).

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