We have used the Illinois Concert C++ system (which supports dynamic, object-based parallelism) to parallelize a flexible adaptive mesh refinement code for the Cosmology NSF Grand Challenge. Out goal is to enable programmers of large-scale numerical applications to build complex applications with irregular structure using a high-level interface. The key elements are an aggressive optimizing compiler and runtime system support that harnesses the performance of the SGI-Cray Origin 2000 shared memory architecture. We have developed a configurable runtime system and a flexible Structured Adaptive Mesh Refinement (SAMR) application that runs with good performance. We describe the programming of SAMR using the Illinois Concert System, which is a concurrent object-oriented parallel programming interface, documenting the modest parallelization effort. We obtain good performance of up to 24.4 speedup on 32 processors of the Origin 2000. We also present results addressing the effect of virtual machine configuration and parallel grain size on performance. Our study characterizes the SAMR application and how our programming system design assists in parallelizing dynamic codes using high-level programming.