Yes, a leaning chimney is dangerous. A chimney that's visibly out of plumb has usually lost its structural support underneath, most often from a shifting or undersized footing, and it can keep leaning until sections of brick separate from the house or the chimney partially or fully collapses. Even a slight lean is worth having checked promptly, since chimneys are tall, heavy structures that don't always give much additional warning once real movement starts.
Chimneys were traditionally built on their own separate footing from the rest of the house, which means they can settle independently of the main structure. A lean usually starts with that footing shifting or settling unevenly, though deteriorated mortar can also let the brick stack itself shift out of true. Either way, the chimney's weight starts bearing unevenly, and that tends to get worse over time rather than stabilize on its own, since an uneven load keeps pushing harder on whichever side is already weaker.
The same frost-line mechanics that affect house foundations apply to chimney footings. If the original footing wasn't set below the local frost line, or wasn't sized properly for the weight of the stack above it, seasonal ground movement from freeze-thaw can gradually push a chimney out of plumb over the years, especially on chimneys built before modern footing requirements were standard practice.
We start by checking how far the chimney has leaned and whether that movement looks active or has settled. From there we inspect the footing itself and the condition of the surrounding brick and mortar. Depending on severity, that can mean stabilizing and repairing from the point of failure, or in cases where the lean has compromised too much of the structure, a full rebuild. A chimney this close to the roofline and often right above a bedroom or living space isn't something to leave leaning and hope it stops.
More on this from Chelo's Brick & Stone.
Chelo's Brick & Stone serves Hillsville, Galax, Wytheville, Fancy Gap, and Independence, VA. Call for a straight answer and a free on-site estimate.