The best way to do this is to trowel on a coat of mortar and then tile over it. It's not that hard, but if you don't think you can do it with a reasonably level finish, then cement board is the next option. Attaching the board to the brick with mechanical anchors is going to be hard and if you don't do it just right, may eventually loosen after you tile, which would be a disaster. If the brick is not painted or polyurethaned, the best and easiest way to attach the cement board is to use a construction adhesive (like Liquid Nails) that is made for use on masonry. It will form a surprisingly strong bond. If it does have a finish on it, you can probably use an adhesive that is made to work with that finish.

Thanks Ventupete for pointing me in the right direction. I might just try that liquid nails option. I am not sure if it can withstand heat. Might have to read up on that.

With regard to the heat, very little of the cement board should really be exposed to any meaningful heat (only the part immediately bordering the firebox opening on the sides and a larger piece directly above the opening). In any event you will have to figure out how you are going to trim the edges that abut the opening. You could install the cement board so that it ends a few of inches away from the opening and fill in the rest with a high temperature mortar mix - typically made from a regular mortar mix with some "fire clay" mixed in. You can get this clay from most building supply stores and it will have directions on it for the optimal mix. You probably want to use this same mix to install the tile along the firebox edges in any event, as regular thinset or mortar tends to crumble after a while from the large temperature swings next to the firebox opening.