Javascript is just a standard, more formally known as ECMAScript. It can be implemented in any language, just like any standard.
Chrome’s Javascript engine, V8, is written in C++.
From the project page:
V8 is written in C++ and is used in Google Chrome, the open source browser from Google.
V8 implements ECMAScript as specified in ECMA-262, 5th edition, and
runs on Windows (XP or newer), Mac OS X (10.5 or newer), and Linux
systems that use IA-32, x64, or ARM processors.
Firefox’s Javascript engine, SpiderMonkey (and now TraceMonkey) is also written in C++. And as maerics below said, Rhino is written in Java.