The statement that is most accurate about the experience of immigrants in the Chesapeake colonies during the seventeenth century is:
The danger posed to new immigrants in the Chesapeake colonies persisted throughout the seventeenth century, especially during the late summer.
This statement aligns with the information provided in the passage, which highlights the high mortality rate among immigrants during their first year and the ongoing dangers in the region as late as 1700, particularly during the late summer.