This is one of those questions where a hundred answers could "sound" right but nobody really knows unless he's standing in front of your "Chimney" and inspecting the structural integrity of it and knows what kind of wall you're intending.

Generally, as the previous reply suggested, a chimney is not and should never be considered a structural aspect of a house. Itís a chimney and should always be treated as a wall meant to surround smoke. A chimney isnít just an upright box wall, itís actually meant to ďdrawĒ smoke and thatís itís first, and normally, itís only priority.

Using Liquid Nails to embed ďall threadĒ into the brick is an interesting idea but consider that ďall threadĒ is usually a relatively (20-24 per inch so it would act more like a metal file) fine course thread and not really intended to bind to an adhesive. And also consider that the brick used for a fireplace is normally soft rather than structural and also old so prone to decay. So the adhesion liquid nails would get from it is nominal at best.

Normally, if the fireplace wall is structurally sound, weíd like to embed an anchor into it using a concrete epoxy and go from there. There are occasions where youíd embed a T-anchor (basically a bolt with a very wide base under a bolt) from one side of the fireplace wall to another but thatís rare. Under most very old house conditions, you could drill a hole in a fireplace wall, run a rope through it, tie a knot on the short end and pull a dozen bricks through with a single tug.

Remember, a chimney is a wall thatís been exposed to very extreme hot/cold, moist/dry conditions for a very long time. Under those conditions, weakened mortar, particularly the standard old lime based mortar, and the brick between it, gravity and happier days are the only things holding it together.