Phil Gormley said he would be "foolish" to rule out more armed police following the Paris terror attacks
He suggested armed police on routine duties may be appropriate in certain circumstances.
The current UK threat level for international terrorism is "severe" meaning an attack is highly likely.
Mr Gormley's predecessor, Sir Stephen House, withdrew armed police from routine patrols following a public outcry about police with guns attending minor incidents.
In a briefing at Police Scotland's Tulliallan headquarters on his second day in the job, the chief constable said Police Scotland "needs to have a very careful look" at armed policing.
"There are lessons to be learned post-Paris around tactics, techniques, the numbers of officers that we have got and their deployment," he said.
"So that is a question that constantly needs to be revisited as the threat level around serious and organised crime alters and the threat level around CT (counter-terrorism) alters."
When asked if he will rule out more armed police in Scotland, he said: "I would be foolish to do so, wouldn't I?
"If the threat from CT and serious organised crime demands that we increase our armed capacity to protect the people of Scotland, then I will need to do that."
He said a decision on deploying armed police on routine patrols "depends what those routine duties are and it depends on the context that they are operating in".
He added: "If the threat level is sufficiently high that we need armed officers to protect the public, then that is what we will need to provide."
Mr Gormley said he respected the Scottish government's decision to maintain its commitment to having 1,000 more police officers than the SNP inherited when it came to power.
But he warned choices would have to be made to protect citizens that involve new techniques and technology as well as police officer numbers and the right mix of resources.
He said Police Scotland "do need to think about what capabilities we need for the future" in relation to police officer numbers.
"Some of that will absolutely be about people, and some of it will be about skills, technical kit and investment," he said.
"Choices will have to be made. I don't want to get into a specific conversation about numbers, but I do think in the next five to 10 years the sorts of demands that police all over the UK will face will require both people and investments and new techniques and technology."
Mr Gormley backed the existing programme of control room closures, which has been slowed down following a damning inspection in the wake of two deaths after a crash on the M9 last year.
He also pledged to close Police Scotland's spiralling Â£25m budget gap before the end of this financial year in April.

A 22-year-old man and a 19-year-old woman have been held following the discovery at Packett Street, Fenton.
Staffordshire Police was called to the scene at 10:00 BST. A force spokesperson said post-mortem tests would take place on Wednesday.
Formal identification of the child has yet to take place.
More on this story and other Staffordshire news
Scenes of crime officers have been examining the property and an alleyway behind it.
Det Insp Dan Ison said: "Our thoughts are with the little girl's family at this time.
"This is a very distressing incident and we are doing all we can to support those affected."
West Midlands Ambulance Service said crews found a child "who was sadly confirmed deceased".
A spokesman said: "They also treated a woman at the scene before she was transported to Royal Stoke University Hospital."
Scotland's new chief constable has said he will deploy more armed police officers if the threat from terrorism or serious crime renders it necessary.
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Two people have been arrested on suspicion of murder after a two-year-old girl was found dead at an address in Stoke-on-Trent.