West Indian planters figure out the plantation system: it makes the land wildly profitable, at enormous human cost.
West Indian planters kill all the Native Americans with overwork and start importing enslaved Africans.
Many planters settle in Virginia, the Carolinas, and George during the 18th century, or send their children there. Plantation owners in Virginia realize they, too, could be making their land wildly profitable.
The laws governing enslaved Africans slowly harden during the 18th century, and after the Revolution, the British legal code is replaced with one that clearly and unambiguously establishes chattel slavery. (Slaves cannot own property, slaves' children are also slaves even if they have free fathers, slaves are legally considered real estate not servants).
Plantations become wildly profitable. This couldn't happen with indentured servants, who have contracts that protect them, or with Native American slaves-- there simply aren't enough of them, and the new United States relates to tribes as separate allied or enemy nations throughout the Indian Wars. Chattel slavery, though, permits masters absolute authority over their slaves' bodies (they can use as much violence as they wish with no legal repercussions). It grants the masters total ownership over the slaves' entire lives. It makes slavery an inheritable condition, so the more children a master's slaves have, the more slaves the master gets. And it makes the slave's labor and all profit thereby, the sole property of the master. No more buying your freedom, when, as a slave, you don't own property!
Scientific racial theory, pioneered by Thomas Jefferson (among others), provides intellectual justification for the enslavement of African-descended slaves. This dovetails very nicely with the strongly hierarchical aristocratic culture among plantation owners.
The economy and culture of the American South becomes structured around slave labor and African-American inferiority by the 1830s: slavery is the South's "peculiar institution". Specifically, the racial (biological, transmittable) inferiority of Africans becomes both proof of why they're "natural slaves," and assures the honor of poor white sharecroppers ("I might have nothing, but at least I'm not a black").
A quick overview of the legal rise of chattel slavery in North America:
In the early colonial period of settlement in the Americas (1500-1690s), the British and French colonies "unfree" labor force was mostly indentured poor whites and some enslaved Africans. The indentured whites were lower-class English and Irish laborers who indentured themselves to earn passage to the New World. Typically, they would work for 4-7 years before earning their freedom and sometimes a parcel of land as well. Enslaved Africans never comprised more than 5% of the colonial North American society, and Native American servants were even rarer.
During this period, enslaved Africans working in the field had more in common than in difference with their indentured Irish or English coworkers. Under British rule, slaves were permitted to hold independent property. (Their bodies and labor might belong to a master, but their property belonged to them). Buying one's freedom was a common and frequently-cited "virtuous" way to leave slavery: for example, Anthony Johnson, a slave to the Bennett family from 1621-1640, buys his and his family's freedom because he is permitted to farm independently. After freeing himself and his family, he buys 250 acres of land and the right to import servants and slaves. He and his sons become eastern Virginia planters. Ironically, Johnson is the "master" in the Johnson v. Casor case, the first case which establishes that people of African descent are "slaves for life," not simply indentured servants. (The short version: Casor has a "seaven or eight yeares" indenture with Johnson; at the end of the time, Johnson won't let him go; Casor runs off and takes an indenture with someone else; Johnson sues for Casor's labor and Casor is declared a slave for life, to work on Johnson's land).
The Casor case reflects the tightening American legal system around people of African descent. Prior to mid-1700, most laws affecting enslaved or indentured Africans were based on British policies for governing non-Christian foreigners. With the 1705 Virginia Slave Codes, slaves are redefined from foreigners to "real estate":
"All servants imported and brought into the Country... who were not Christians in their native Country... shall be accounted and be slaves. All Negro, mulatto and Indian slaves within this dominion... shall be held to be real estate."
Sources:
Ira Berlin, Many Thousands Gone: The First Two Centuries of Slavery in North America.
Hugh Thomas, The Slave Trade: the Story of the Atlantic Slave Trade, 1440-1870.
Collin A. Palmer. Passageways: An Interpretative History of Black America, Vol I
Ed. Vincent Carretta, Unchained Voices: an Anthology of Black Authors in the English-Speaking World of the Eighteenth Century.