A book consists of a number of half-planes (pages) sharing a common boundary line (the spine). A book embedding of a graph embeds the vertices on the spine and each edge in some page so that each page contains a plane subgraph. The width of a page is the maximum number of edges that intersect any half-line perpendicular to the spine in the page. The pagewidth of the embedding is the maximum width of any page, and the pagewidth of the graph G is the minimum pagewidth of any book embedding of G in a book having a minimum number of pages for G. The author presents an O(n log n) time algorithm for embedding an n-vertex outerplanar graph with small pagewidth. The algorithm embeds any d-valent outerplanar graph in a two-page book with pagewidth O(d log n). This result is optimal in pagenumber for the stated pagewidth and optimal in pagewidth (to within a constant factor) for the class of outerplanar graphs. There is application to fault-tolerant arrays of VLSI processors: any outerplanar graph can be implemented in small area, in a fault- tolerant fashion.