How can I create a new primitive type using C++11 style strong typedefs?

There are no strong typedefs in C++11. There is support for units with <chrono> but that is a totally different thing. Nobody can agree on what behaviour strong typedefs should have, exactly, so there has never been a proposal for them that got anywhere, so not only are they in neither C++11 nor C++14, there is no realistic prospect at this time that they will get into any future Standard.

C++ compilers generally expect the command line option -std=c++11 (or -std=c++0x for slightly older ones, respectively) to activate C++11-support.

not supporting C++11 style at all.

No, it perfectly does. GCC 4.7.2's support can be checked here. To activate some experimental features, pass -std=gnu++11.

And Clang 3.4 actually supports pretty much everything in C++11 and already much out of C++1y.

Not sure this is what you want, it is ugly, but it works :) You can wrap the type into a template class,

template <typename T, int N> // N is used for tagging
struct strong_typedef
{
    using strong_type = strong_typedef<T,N>; // typedef for the strong type
    using type = T; // the wrapped type
    T value; // the  wrapped value

    strong_typedef(T val): value(val){}; // constructor
    strong_typedef(){value={};}; // default, zero-initialization

    // operator overloading, basic example: 
    strong_type& operator+(const strong_type& rhs)
    {
        value+=rhs.value; 
        return *this;
    }

    // display it
    friend ostream& operator<<(ostream & lhs, const strong_typedef& rhs)
    {
        lhs << rhs.value;
        return lhs;
    }
};

then use it as

// these are all different types
strong_typedef<double, 0> x = 1.1; 
strong_typedef<double, 1> y = 2.2;
strong_typedef<double, 2> z = 3.3;

std::cout << x + x << std::endl; // outputs 2.2, can add x and x
// cout << x + y << endl; // compile-time ERROR, different types

x, y and z are 3 different types now, because of the different N-s used in the template. You can access the type and value using the fields type and value, like x::value (will be double 1.1). Of course if you directly typedef the struct_typedef::type, you're back to square one, as you are losing the strong type. So basically your type should be strong_typedef and not strong_typedef::type.