Tear the chard leaves off the stems. Slice the stems into bite-sized pieces and roughly chop leaves.
Heat the oil in a large skillet over medium-high heat. Add the sliced onion and chard stalks and saute for 2 minutes, or until beginning to brown. Add the salt and turn the heat down to medium.
Sweat for another 8 to 10 minutes, stirring often. Add the garlic and cook for 1 more minute.
Add the broth, bring to a simmer, and place the greens on top. Once they are wilted enough to fold in (about 2 minutes), stir them into the onions.
Saute for another 5 minutes, or until the chard is soft. If there is still liquid, turn the heat to high to reduce it.
Turn off the heat and stir in the lemon zest, lemon juice, and red pepper flakes. Serve hot.