Pascal's Triangle is, without question, the most well-known triangular array of numbers in all of mathematics. A well-known algorithm for constructing Pascal's Triangle is based on the following two observations. The outer edges of the triangle consist of all 1's. Each number not lying on the outer edges is the sum of the two numbers above it in the preceding row. Pascal's Triangle is ordinarily introduced to students in connection with its intimate relationship to the Binomial Theorem. In this article, the author presents a method for generalizing Pascal's Triangle and then shows that Pascal's Triangle can be viewed as an element of an infinite set of triangular arrays of numbers called "Pascal's Infinite Set of Triangles." The material presented in this article is accessible to students acquainted with Pascal's Triangle. (Contains 5 figures.)