Does the "Set next statement" feature exist in Chrome's Dev Tools or in Firebug?

While Chrome DevTools doesn't have "Set Next Statement", you can more explicitly define next statement by just editing the JavaScript while it's paused at the breakpoint.

I've made a short screencast for you to show Chrome DevTools Live Edit + Breakpoint Debugging.

In essence: while at a breakpoint, live edit your script by clicking into the Scripts panel and making changes. Hit cmd + s to save. Then walk through that code with its new changes. Far more powerful than just bypassing code, you could be adding new functionality as well.