You are right window.showModalDialog() doesn't work with the latest updated version of Google Chrome, i too faced this problem in my project.
You can have a number of solutions for that :-
1. The easiest one is window.open();
Pros:- Easy to handle and use.
Cons:- You can still work on the parent page while the pop-up window is opened.
2. The Efficient solution is to use jQuery dialog control.
For better understanding of jQuery dialog control you can refer the