Despite the significant effort that often goes into securing critical infrastructure assets, many systems remain vulnerable to advanced, targeted cyber attacks. This paper describes the design and implementation of the Trusted Dynamic Logical Heterogeneity System (TALENT), a framework for live-migrating critical infrastructure applications across heterogeneous platforms. TALENT permits a running critical application to change its hardware platform and operating system, thus providing cyber survivability through platform diversity. TALENT uses containers (operating-system-level virtualization) and a portable checkpoint compiler to create a virtual execution environment and to migrate a running application across different platforms while preserving the state of the application (execution state, open files and network connections). TALENT is designed to support general applications written in the C programming language. By changing the platform on-the-fly, TALENT creates a cyber moving target and significantly raises the bar for a successful attack against a critical application. Experiments demonstrate that a complete migration can be completed within about one second.