std::mt19937 and std::uniform_real_distribution returning boundary value every time

OK, so I've got some RNG code that (when all is said and done) boils down to this:

#include <limits>
#include <random>
#include <chrono>
#include <iostream>

double randomValue() {
    // Seed a Mersenne Twister (good RNG) with the current system time
    std::mt19937 generator(std::chrono::system_clock::now().time_since_epoch().count());

    std::uniform_real_distribution<double> dist(
        std::numeric_limits<double>::lowest(),
        std::numeric_limits<double>::max()
    );

    // Problem lives here
    for (unsigned int i = 0; i < 30; i++)
        std::cout << dist(generator) << "\n";
}

The output from this is 30 lines of inf. Why?

Compiling with g++ Debian 4.9.2-10, using -std=c++11 and no other flags. And, before anyone else comments on it, I'm using the built-in Mersenne Twister-based RNG because my application requires high-quality random numbers, and seeding it with the system time (so no, it's not just the same seed over and over again).