The Greenpeace activists are protesting against nuclear power.
They chained themselves up inside the Honore Mercier building by the legislature, where the premier's office is. Charest was in Toronto when the protest happened.
The protesters are spreading their anti-nuclear message in advance of the one-year anniversary of Japan's earthquake, which prompted global fears of a catastrophe at the Fukushima plant.
In Quebec, the provincial government is now deciding whether to refurbish the Gentilly nuclear facility, near Trois-Rivieres; the facility produces only a tiny fraction of Quebec's energy.
The protesters say that if it's this easy for them to penetrate the premier's office, how can the government possibility guarantee that it can keep the nuclear site safe.
National assembly security guards are now considering ways to expel the protesters without using force.
Charest said in Toronto that the province would like to refurbish the Gentilly plant but is awaiting a report from the Canadian nuclear security regulator which is expected to contain recommendations in the wake of the Fukushima disaster.
"We will want to see that report as we move ahead with the Gentilly project," Charest told reporters after a speech. "It will depend on what will be in there but we would like to see Gentilly refurbished."