Yes, it is true. According to Euclidean geometry, for any given line and a point not on that line, there exists exactly one line that can be drawn parallel to the original line through that point.
This principle is a part of what is known as the Parallel Postulate, which is one of the key axioms in Euclidean geometry. The essence of the postulate states that if you have a line and a point outside of that line, the point will have a unique line parallel to the original line passing through it. This unique parallel line will never intersect the original line, regardless of how far they are extended.
To visualize this, imagine a straight horizontal line. If you take a point above or below this line, you can draw just one straight line that runs parallel to the horizontal line through the point. Any other line that you might draw through that point will eventually cross the horizontal line, thus failing to be parallel.
This concept is fundamental to the structure of Euclidean geometric spaces and helps to establish the behavior of parallel lines, as well as serving as a foundation for more complex geometrical concepts.