I’m adding a late answer after nearly 3 years because with the current Chrome Dev Tools, neither approach work if you have an Array or even just a nested Object property in that variable, following both answers you’ll just end up copying a string with a lot of Array[size] or Object strings interleaved in the actual object value, completely useless for complex object hierarchies.
The suggested approaches are ok if you just need to manually navigate through the value but not if you need to copy it as requested in the question.
What i recommend instead, especially if you need to copy the watched value to use it as the content of a new variable, is to dump it to console after it has been stringified.
Show the Javascript console and type:
console.log(JSON.stringify(my_watched_var))
This way the complete structure will be displayed in pure Javascript, a fully reusable/copyable way.