Software testing remains the most widely used methodology for validating quality of code. However, effectiveness of testing critically depends on the quality of test suites used. Test cases in a test suite consist of two fundamental parts: (1) input values for the code under test, and (2) correct checks for the outputs it produces. These checks are commonly written as assertions, and termed test oracles. The last couple of decades have seen much progress in automated test input generation, e.g., using fuzzing and symbolic execution. However, automating test oracles remains a relatively less explored problem area. Indeed, a test oracle by its nature requires knowledge of expected behavior, which may only be known to the developer and may not not exist in a formal language that supports automated reasoning. Our focus in this paper is automation of test oracles for clients of widely used Java libraries, e.g., java.lang and java.util packages. Our key insight is that Javadocs that provide a rich source of information can enable automated generation of test oracles. Javadocs of the core Java libraries are fairly detailed documents that contain natural language descriptions of not only how the libraries behave but also how the clients must (not) use them. We use large language models as an enabling technology to embody our insight into a framework for test oracle automation, and evaluate it experimentally. Our experiments demonstrate that LLMs can generate oracles for checking normal and exceptional behaviors from Javadocs, with 98.8% of these oracles being compilable and 96.4% accurately reflecting intended properties. Even for the few incorrect oracles, errors are minor and can be easily corrected with the help of additional comment information generated by the LLMs.