Rinse the tomatoes, jalapeños, cilantro, and limes under cool running water and dry them well. Set your cutting board on a damp paper towel so it does not slide, and place the mixing bowl, knife, spoon, juicer, and gloves within easy reach.
Cut each tomato in half lengthwise, cut out the hard core, and scoop out the seeds and watery gel with a small spoon. Lay each half cut side down, slice into 1/4 inch strips, then turn and cut crosswise into 1/4 inch cubes. Let the diced tomatoes drain in a fine mesh strainer for about 5 minutes, then add them to the mixing bowl.
Peel the onion, keep the root end intact, and place it flat side down. Slice vertically into thin strips, then cut across to make a fine 1/4 inch dice. Rinse the diced onion under cold water for about 30 seconds, pat dry, and add it to the bowl with the tomatoes.
Put on disposable gloves, slice off the stems, and cut each jalapeño in half lengthwise. Scrape out the seeds and white ribs with a small spoon, slice the halves into thin strips, then mince into tiny rice-sized pieces. Start with 1 jalapeño for mild to medium heat and add the second only if you like it spicy, then stir into the bowl.
Gather the cilantro into a tight bunch and trim off the thick, woody bottom stems. Slice through the leaves and tender stems, rocking the blade back and forth until finely chopped. Measure out 1/2 cup and add it to the bowl, avoiding over-chopping so the cilantro does not bruise and turn dark.
Roll the limes firmly on the counter, cut them in half, and squeeze with a citrus juicer until you have 2 tablespoons of juice. Pour the lime juice over the vegetables, sprinkle in the kosher salt, and gently fold everything together with a rubber spatula without mashing the tomatoes. Taste and add more salt or lime juice if needed.
Cover the bowl and let the pico de gallo rest at room temperature for 30 minutes so the flavors can blend, or chill it in the refrigerator for the same amount of time if you prefer it cold. Stir gently, taste once more, and adjust the salt, lime juice, or jalapeño until bright and balanced.
Transfer the pico de gallo to a serving bowl and set it out with a big basket of tortilla chips. Use a slotted spoon when serving to leave extra juices behind, and store any leftovers in an airtight glass container in the refrigerator right after the meal.