Isso porque o Chrome é um navegador de 32 bits, que não é suportado pelo JRE 7. De sua FAQ :
Q: Should I install the JRE or the JDK?
A: If you plan to run Java applications, install the Java Runtime Environment (JRE). The JRE is also referred to as Oracle Java. Once you have installed the JRE, you can launch Java applets and applications by double-clicking JAR files, JNLP files, and via the browser. Note that 32-bit browsers, such as Firefox in 32-bit mode, and Chrome, are not supported by the JRE.