Dripping on ceiling from roof?

Woke up this morning to hear dripping noise coming from ceiling. Walked around housing to investigate and heard the dripping hitting the ceiling above staircase (it is a void space above this). Went up into loft and couldn't see any water running. Then a damp patch formed on the ceiling. Cut open plasterboard to see water dripping down through a hole from ceiling above (i.e. ceiling above void space). Went back into loft, and noticed that where the hole is in ceiling, is right next to the chimney stack/brest. Could water be running down from chimney? How would this be repaired to stop water dripping?