Two-way chippers are illegal. The United States Golf Association, the governing body for the sport in North America, sets forth the applicable standard in Rule 4-1d. It states that a clubhead shall have "only one striking face except putters with similar faces."
Definition of Putter
Since putters are the only clubs that can have two striking faces, golfers can use either side of a putter that has identical faces to strike the ball. This exception is intended to legalize blade putters that are identical on both sides. However, the USGA's "Rules of Golf" require putters to have less than 10 degrees of loft. Two-way chippers don't qualify as putters, since typical chippers have roughly 30 degrees of loft on each of the faces, equivalent to a 5-iron or 6-iron.
Usefulness of Two-Way Chipper
While the illegality of two-way chippers has reduced their popularity – and prevents them from being used in official tournaments – some golfers still use them in recreational rounds for their versatility. You can chip with them and hit shots left-handed or right-handed if your ball is near an obstacle that prevents you from addressing the ball as you normally would.
While you can use illegal clubs such as a two-way chipper in social play if no one in your group objects, doing so violates the rules and affects the accuracy of your handicap. After all, if your group doesn't mind, you could tee off with a baseball bat or hockey stick. In terms of the official Rules of Golf, however, the social play "exception" is meaningless. In any competition played under the Rules of Golf, Rule 1-3 states, "Players must not agree to exclude the operation of any Rule or to waive any penalty incurred." If you violate this rule, you incur the harshest of penalties – both players are disqualified in match play, or all players in the group are disqualified in stroke play.
Few golf manufacturers make two-way chippers, but you can find the standard single-face chippers. They range from as little as $20 for an inexpensive model to as much as $100 or more for major brands such as Odyssey.