We present an isosurface meshing algorithm, DELISO, based on the Delaunay refinement paradigm. This paradigm has been successfully applied to mesh a variety of domains with guarantees for topology, geometry, mesh gradedness, and triangle shape. A restricted Delaunay tri- angulation, dual of the intersection between the surface and the three dimensional Voronoi diagram, is often the main ingredient in Delaunay refinement. Computing and storing three dimensional Voronoi/Delaunay diagrams become bot- tlenecks for Delaunay refinement techniques since isosur- face computations generally have large input datasets and output meshes. A highlight of our algorithm is that we find a simple way to recover the restricted Delaunay triangula- tion of the surface without computing the full 3D structure. We employ techniques for efficient ray tracing of isosurfaces to generate surface sample points, and demonstrate the ef- fectiveness of our implementation using a variety of volume datasets.