Heat a heavy-based griddle pan. Thickly slice the plum tomatoes and then lightly brush with olive oil. Add to the heated pan and cook for about 5 minutes until nicely marked. Transfer to a plate and keep warm. Brush the bread with a little more oil and toast on the same pan until nicely marked.
Meanwhile, heat a little olive oil in a large non-stick frying pan and crack in the eggs. Scatter over the garlic and chilli, if using and cook for a couple of minutes, spooning the hot oil over the egg yolks until they are cooked to your liking.
Place the griddled bread on warmed plates and quickly arrange the griddled tomatoes on top.
Scatter the chives into the egg pan and sprinkle over the balsamic vinegar. Season generously, then slide the eggs on to the tomatoes and drizzle over any pan juices. Add a small pile of the salad to each plate to serve.