In recent years, the AI wave has grown rapidly in software development. Even novice developers can now design and generate complex framework-constrained software systems based on their high-level requirements with the help of Large Language Models (LLMs). However, when LLMs gradually "take the wheel" of software development, developers may only check whether the program works. They often miss security problems hidden in how the generated programs are implemented. In this work, we investigate the security properties of framework-constrained programs generated by state-of-the-art LLMs. We focus specifically on Chrome extensions due to their complex security model involving multiple privilege boundaries and isolated components. To achieve this, we built ChromeSecBench, a dataset with 140 prompts based on known vulnerable extensions. We used these prompts to instruct nine state-of-the-art LLMs to generate complete Chrome extensions, and then analyzed them for vulnerabilities across three dimensions: scenario types, model differences, and vulnerability categories. Our results show that LLMs produced vulnerable programs at alarmingly high rates (18%-50%), particularly in Authentication & Identity and Cookie Management scenarios (up to 83% and 78% respectively). Most vulnerabilities exposed sensitive browser data like cookies, history, or bookmarks to untrusted code. Interestingly, we found that advanced reasoning models performed worse, generating more vulnerabilities than simpler models. These findings highlight a critical gap between LLMs' coding skills and their ability to write secure framework-constrained programs.