Chaperons were a necessary part of life in a young upper or middle class woman's world. A chaperon was almost always female and frequently an older relative such as the woman's mother, a maiden aunt, or an older married or widowed woman of the family. Other possible chaperons were trusted servants and governesses. Under no circumstances would an unmarried woman ever be alone with a man who was not a relative or her fiancé, and a father generally left this sort of thing to the mother, and so male chaperons were rare if not non-existent.
Until she was engaged, however much an upper class woman might resent her chaperon, there was no honest way to escape her. Even after her engagement, the only man she could be around alone that was not a relative was her fiancé, and even then only for limited periods of time.
Who Had a Chaperon
Every unmarried upper class woman would be chaperoned at all times outside of her parents' home. Any middle class woman from a family with an eye towards the upper class would also be chaperoned, just as an upper class woman would be. Because innocence and virtue were even more valuable than beauty, these traits were jealousy guarded by parents and guardians of young women.
Because chaperons were so common, no one thought it odd to have one present. A gathering of wealthy young women could easily have as many chaperons present as there were girls. These women were a constant presence and a part of everyday life.
Innocence and Virtue
The concepts of innocence and virtue went beyond mere virginity. Physical contact was considered highly intimate in and of itself, and so was forbidden under most circumstances. A man could offer his arm to help a young woman over a rough patch if they were out walking and dance was socially accepted, but other than that even so innocent a gesture as holding hands was forbidden to a couple that was not yet engaged.
When a couple did become engaged they had more freedom, but were still expected to stay strictly within the realms of propriety. The fiancé usually took the chaperon's place, making sure his future bride's honor was still protected.
Escaping the Chaperon
In most cases, young women were just as careful in protecting themselves as their parents were. A lady was raised to be a wife and mother, and knew that her only chance of any change in her life was marriage. As such, a woman would be very careful of her reputation -- after all, if anything unacceptable was to occur, it would be her status that was damaged and not the man's.
The only appropriate way to escape from a chaperon was to become engaged, at which point a lady's honor was given into the care of her fiancé. Even then, an honorable man would take great care to make sure that his future bride's honor was cared for and not attempt to seduce her or in any other way take advantage of what privacy their engagement offered. He would also never break the engagement, as the time his fiancé had spent alone with him would then damage or even ruin her reputation, even though she would still be a virgin.
Less honestly, a young woman might evade a chaperon who was not as watchful as she should be. While most young woman would not do so no matter how a chaperon grated, it was possible to slip out of sight of a distracted or otherwise occupied chaperon. It would likely be more common for a child to escape her watcher than a woman who had come out into society, because it would tarnish her reputation less than it would for a courtable woman to do so.