
(Paint skills, yo-->)
This is a variant that I invented with a few friends several years ago. Since then I have introduced it to a handful of people. We have played enough times to be sure that it does make for an exciting and playable game. Also, we have been able to patch up most of the incosistencies/loopholes in the rules; however a few may still remain, and anyway I probably did not remember most of them in the short time it took me to jot this down. Please point out anything that you feel needs clarification or revision. Hopefully I will someday be able to form a more complete ruleset. That way we will have a go-to source to avoid all those bickerings and petty arguments 
1) General. In addition to a normal set of 16, White starts with two portals on e4, d4, and Black starts with two on e5, d5. The easiest way to represent these is by using upside-down rooks and playing without normal rooks, although a complete game should use rooks too. They move like kings, and movement of a portal takes up a turn. Movement of portals does not conflict with movement of pieces: They may occupy the same square as a friendly or enemy piece, be moved through by a piece, be moved onto the square of a piece, and be moved out from under a piece. The only restriction is that two portals, friendly or enemy, may never occupy the same square.
2) Movement between portals. Movement between two portals ('teleportation') does not distinguish between owner. Teleportation is free, and the player still moves the piece during that turn. The player may chose either: to teleport a piece from one portal to another and then move the piece normally, or to move (capture) onto a portal normally and then teleport. Of course, a player may also elect to ignore a portal and simply move the piece normally for their turn. Also, a piece may teleport, then move normally, then teleport again. (This may seem redundant, but matters in the case of a capture, described below.)
3) Victory conditions. The game ends when a player is unable to prevent their king being captured next turn, similar to chess.
4) Capturing. Normal captures may occur regardless of whether there is a portal on the capturing square. If there is a portal there, the player has the option of then transferring the capturing piece to another portal. Also, a piece may teleport then capture normally, and even teleport-capture-teleport. However, a piece may NOT capture a piece on a portal by teleporting onto the portal--the portal is 'blocked' by the enemy piece. (If not for this rule, then a piece could simply wipe out all enemy pieces on portals, and then make a normal move, all in the same turn.) Thus one useful way of projecting the queen's power is placing one portal on d1, then moving the other portal out to attack other pieces on portals: In one turn the queen may teleport out, move normally to capture a piece on a portal, than teleport back to safety.
5) Promotion. A pawn is promoted instantly whenever it reaches the far rank, whether by teleportation or movement. In fact, one common technique is to place one portal on the second rank and one on the eighth, then instantly queen a pawn that can even move on the same turn. However this requires that the forward portal find a square deep in the opposite camp that the opponent is unable to block with their own pieces.
6) Miscellaneous. For simplicity, castling and en passant are simply not allowed; they have no significant use anyway.