This vertical sliver of whitespace before each character is almost certainly a characteristic of the font you're using to render this <h1>
text. Font designers manage inter-character spacing by putting some of the space at the end of characters and some of it at the beginning. They typically optimize this for both optical (eyeball) alignment at the beginnings and ends of justified lines and also for nicely balanced intra-word spacing.
If you must get rid of it, there are some things you could try.
Negative tracking. Try a small negative CSS
letter-spacing
attribute like.05em
. This will cram your characters a little closer together. Be subtle with this effect.A boldface font choice. Often the font designer makes the font bold by thickening the strokes symmetrically about their centerline. This may eat up a bit of the leading whitespace.
As a last resort, render the text into a graphic (png or gif) and then trim its edge. This won't look very good.