Expanding somewhat on the answer of AlexP, the earliest domestic horses were too small to be ridden in the manner we do, and according to "The Horse, The Wheel and Language", the use of wagons and chariots is exactly how the Proto Indo Europeans spread from the Ukrainian grasslands to effectively conquer the world from India to the Atlantic shores of Europe.

Chariots had advantages for their users that warriors on foot or even riding bareback would not be able to replicate. A chariot allowed the user to wear armour or be protected by a shield with less expenditure of energy than a walking man, while the small horses of the era would not allow for the use of heavy armour. A warrior as part of a chariot team (most ancient chariots had a separate driver) could focus on using his weapon from an elevated platform (giving huge advantages), would be moving faster than a dismounted man but could also engage in using weapons more effectively than a mounted person, since they would not be using muscular strength to control the horse at the same time they were using a bow or javelin.

The Proto Indo Europeans likely developed the idea of a chariot as an extension of wagon technology, realizing that the high platform of wagons allowed them to see farther than on foot, and a light wagon drawn by horses could move fast enough to allow them to keep up with their flocks and protect them from marauding wolves and other predators. It would be a short step to go from wolves to "other" tribes and settled farmers on their treks...

Now the Proto Indo Europeans were actually pre to very early Bronze age (and interacted with people's on the edge of the Steppes who had Bronze technologies), but the general effect of a people who could effectively move long distances through the use of wheeled transport (logistically, the use of wagons allowed the Proto Indo Europeans to move as entire families, clans and tribal groups rather than just raiding parties. Bringing your family, herds of sheep, tools and supplies made the Proto Indo Europeans far more versatile and effective when reaching areas they felt were suitable to settle in, since they arrived all at once with everything).

Reconstruction of a Proto Indo European wagon

We also should remember that Proto Indo European people were not using the sort of light war chariots that we visualize from Egyptian art or watching the movie Ben Hur - these would effectively have been smaller versions of the sorts of wagons that the rest of the clan was following in, and likely carrying a three man crew (driver, archer/spearman and shield bearer). While we would see this as ridiculously slow by modern standards, for early Bronze age farmers standing on the edge of the field, these would be moving at amazing speeds. Bronze age armies on foot would be rapidly encircled and shot down by arrows and spears while unable to move fast enough to either counter or escape from the invaders.

Reconstruction of a Proto Indo European chariot

So it is entirely possible, and indeed probable that chariot warfare was practiced by the Proto Indo European peoples as they spread from their ancestral homelands in Ukraine to India, the Middle East and Europe.

Expanding somewhat on the answer of AlexP, the earliest domestic horses were too small to be ridden in the manner we do, and according to "The Horse, The Wheel and Language", the use of wagons and chariots is exactly how the Proto Indo Europeans spread from the Ukrainian grasslands to effectively conquer the world from India to the Atlantic shores of Europe.

The spread of the Proto Indo Europeans

Chariots had advantages for their users that warriors on foot or even riding bareback would not be able to replicate. A chariot allowed the user to wear armour or be protected by a shield with less expenditure of energy than a walking man, while the small horses of the era would not allow for the use of heavy armour. A warrior as part of a chariot team (most ancient chariots had a separate driver) could focus on using his weapon from an elevated platform (giving huge advantages), would be moving faster than a dismounted man but could also engage in using weapons more effectively than a mounted person, since they would not be using muscular strength to control the horse at the same time they were using a bow or javelin.

The Proto Indo Europeans likely developed the idea of a chariot as an extension of wagon technology, realizing that the high platform of wagons allowed them to see farther than on foot, and a light wagon drawn by horses could move fast enough to allow them to keep up with their flocks and protect them from marauding wolves and other predators. It would be a short step to go from wolves to "other" tribes and settled farmers on their treks...

Now the Proto Indo Europeans were actually pre to very early Bronze age (and interacted with people's on the edge of the Steppes who had Bronze technologies), but the general effect of a people who could effectively move long distances through the use of wheeled transport (logistically, the use of wagons allowed the Proto Indo Europeans to move as entire families, clans and tribal groups rather than just raiding parties. Bringing your family, herds of sheep, tools and supplies made the Proto Indo Europeans far more versatile and effective when reaching areas they felt were suitable to settle in, since they arrived all at once with everything).

Reconstruction of a Proto Indo European wagon

We also should remember that Proto Indo European people were not using the sort of light war chariots that we visualize from Egyptian art or watching the movie Ben Hur - these would effectively have been smaller versions of the sorts of wagons that the rest of the clan was following in, and likely carrying a three man crew (driver, archer/spearman and shield bearer). While we would see this as ridiculously slow by modern standards, for early Bronze age farmers standing on the edge of the field, these would be moving at amazing speeds. Bronze age armies on foot would be rapidly encircled and shot down by arrows and spears while unable to move fast enough to either counter or escape from the invaders.

Reconstruction of a Proto Indo European chariot

So it is entirely possible, and indeed probable that chariot warfare was practiced by the Proto Indo European peoples as they spread from their ancestral homelands in Ukraine to India, the Middle East and Europe.