A few hundred yards away a sniper had opened up with a sub-machine-gun, while some other maniac, hidden in the detritus that used to comprise the local neighbourhood, was firing back as if his life depended on it, which it probably did. Matters were made more alarming by a Russian soldier at the roadblock where we were waiting, who tossed a vodka bottle in the air and tried to shoot it down, blasting away with his rifle. He missed; it fell to the ground, another addition to the dozens of other bottles and beer cans strewn around by the soldiers in their effort to drown their fear and isolation in this unhappy place.
But this is Grozny, where such battles are frequent enough to be regarded as commonplace, undeserving of panic. As the snapping sound of gunfire continued, many in the queue of traffic calmly turned round and drove away in search of another route out of town. Others - like Said, my taxi- driver - persuaded the soldiers to let him press on, driving through the area looking no more ruffled than a motorist on a Sunday jaunt.
If there was a Nobel prize for doggedness, it would go to the residents here, who have conjured up a sense of normality, of routine, even. So exhausted are they by fear, and daily overdoses of adrenalin, they often seem immune to both.
Half an hour before the shooting, which happened on the outskirts, I watched a morning commuter train pull in to the city's central station. Yes, there are commuters here, even though Grozny was only two weeks ago turned into a battleground yet again when hundreds of separatist rebels arrived. Out into the spring sunshine stepped scores of men and women, with the same purposeful air that you see among the tide of humanity at Paddington or King's Cross every morning. They filed off through the sea of litter, past pools of water that block the roads, and through the ruined boulevards that used to comprise the heart of this once handsome, pastel-tinted, city.
As we headed towards the marketplace, another gunman was also beginning his morning's labours, in the rooftops no more than a few hundred yards away. It was hard to tell what he was shooting at, or why; Grozny's war is not only between the rebels and Russians, supported by Moscow-backed Chechen forces from the puppet government of Doku Zavgayev. It also embraces a tangle of warring clans.
The crowd did not so much as miss a step, let alone scatter. "We have to live," said my guide, a middle-aged Chechen, when I asked why people were willing to brave such hazards. "What do you expect us to do: sit at home and go hungry?"
There is, at present, no risk of that, at least for those with money. The market was groaning with produce, from Snickers bars to lemons, tangerines, onions, potatoes, chicken, and legs of lamb. Where there is a shortage of essential goods, residents make them themselves. Along the roadsides there are large glass jars of home-made petrol on sale.
At a kiosk next to the government building - which has been turned into a fortress, surrounded by dug-in armoured vehicles - there were copies of Soldier of Fortune magazine. Although Russians have lost hundreds of men in this war, their appetite for tales about weaponry and derring-do is mysteriously insatiable. (Whether the soldiers, who are miserably paid, can afford such frivolities is another matter: one group was so short of food that they shot and kebabed the pet dog belonging to the Organization for Security and Co- operation in Europe.)
There are luxuries, too. Most shops and businesses are destroyed, but you can still buy an embroidered dress or a pair of patent-leather high heels. There is clearly a demand: despite the thick mud and filth, many of Grozny's women are as well groomed as Wall Street executives.
Yet, for all this outward calm and resourcefulness, there are wells of hatred, scars too deep to justify any optimism about peace in the Caucasus. After passing the gun battle at the road-block, Said drove me to the airport at Vladikavkaz in the neighbouring republic of Ossetia. A few miles from our destination, he suddenly became agitated and sweaty.
"I can't go any further, it's the Ossetians," he explained. "They loathe us Chechens," he said, putting his finger to his head and pulling an imaginary trigger. Why? Because they were friends with the IngushFD, with whom the Ossetians fought a war in 1992.
It was only after we found an Ingush policeman, armed with a semi-automatic rifle, as an escort that he agreed to go on.
They are getting by here - miraculously well, in the circumstances - but it is hard to believe they will ever get along.