But it's not some sinister insect attack - it's part of a city bid to help stem the decline in the numbers of these vital insects.
And to make sure they have settled into their new home, council leader Gordon Matheson clambered on to the roof of the building to check out their hives.
In recent years honeybee numbers have been hit by disease, increased pesticide use, lack of foraging and climate change.
Now sustainable Glasgow has introduced two colonies on the flat roof of the Chambers high above George Square.
The new arrivals, which have two insulated hives to keep them warm in winter, have already proved a huge hit with council staff who have volunteered in swarms to look after them.
The appeal to be trained in hive management was so popular there is now a waiting list.
The bees will travel as far as three miles from their new homes to find pollen and are expected to visit flowers in George Square and Glasgow Green as well as flying to other parks.
The wax they produce will be used as polish for the Satinwood Suite which is lined with satinwood imported from Queensland.
What the council does with the honey produced will depend on its quality and quantity.
Mr Matheson said: "Bees are exceptionally important to the food chain.
"They pollinate a third of the food we eat and also pollinate trees which help reduce air pollution by taking in carbon dioxide and releasing oxygen.
"Sadly, their numbers have dropped dramatically in recent years so Sustainable Glasgow is doing its bit to help reverse that decline by installing these two hives right in the centre of the city."
Waren Bader of PlanBee, which has provided the hives and training said: "Bees can be safer in a city than in the countryside where a lot of farmers use pesticides.
"No-one need worry about them being on the roof of the City Chambers ... unless they are a flower."