Safe lacquer to use on wood chess pieces?

Not bad! I'm very pleased with the shellac coating. It's just a simple chess set made of a rather cheap kind of wood. Some of the pieces lean to one side. But my precious wife brought it all the way from the Philippines, so I enjoy using it to study great games from the past.

Yes, I added the notation along the sides. I'm old and grew up on a different type of notation, and I have trouble remembering algebraic. 

Thanks again to everyone who made suggestions.

Bele

For reference, Frank Camaratta recommended using Liberon Black Bison Clear Paste Wax on chess pieces. Wipe it on, wait 20 minutes minimum, wipe it off. I typically wipe it on and wait a few hours. Gives a nice shine and helps protect the wood.

I realize this is an old post, but I will comment for future readers.

I recommend sanding smooth and then several coats of Tru-Oil which is a Gun stock finish.  A mix of linseed and mineral oil.  It dries fast. After sanding, apply several coats lightly sand, and a apply a few more.  You could easily do 10 coats or more in a day.  Apply outside as there is an odor.  I use it on chessboards.

Thanks for the additional recommendations! It's nice to know that there are many ways to make a simple set of chess pieces look more beautiful.  Especially for those of us who cannot afford an expensive chess set.

For me, the look and feel of a chess set are a big part of my enjoyment of the game.

Rubio monocoat. Apply a second coat of universal maintenance oil from them. Then polish with furniture wax. 

A couple light applications of natural shellac (1:4 dilution ratio with methylated spirit or grain alcohol by weight) over a well-polished surface would give you by far the best surface you'd ever see on a piece of wood. In my experience no other finish ever comes close in terms of look and feel (and sometimes smell).

Best to apply one coat, lightly sand it & polish on a lathe, then apply two more. Each coat is touch-dry in 15 min between applications but leave the pieces overnight before you use them for playing.

Failing that, I'd go the natural oil route (tung oil would be my pick), but oils are a league or two below shellac in my books.

Anything that forms a thick, visible film will make the pieces look & feel cheap, and best avoided.

At the end of the day, it's not what finish you apply or how you apply it, but it's down to the quality of your wood polishing prior & during application.

Here's a before & after snap.