Hmm. Are they? I decided to look it up. The short answer is: No.
The longer, but still summing up, is: There's a group tied into the U.N. that decided back in the mid-80s to hold a moratorium on killing whales until they could figure out what the heck was going on with the whales. What is a sustainable number? How far off from that are we? Where are the whales? What else is effecting them? Are we contributing to it? Those kinds of things. Getting some of these answers unfortunately requires killing whales to gather the data. (Technology limit.) As soon as the moratorium was declared Japan (and others) immediately applied to the big group for permits so they could kill whales for 'scientific purposes'.
Now here's the thing. The group can make recommendations BUT it is up to each individual country whether they will give these permits to /themselves/. Got that? They are required to give an outline of the goals of their research and to share the results within one year of killing the whales - but other than that nobody can say boo. Japan has told itself that it must make full use of any whale it kills for scientific purposes (but it wasn't mentioned what that entails).
All the other countries in the group have told Japan to stop the killing and to find no-lethal means of their collecting data. However they also acknowledge that they have learned a lot from Japan's research.
The biggest point of contention is that Japan is killing whales in an area everyone has agreed is a sanctuary. So /technically/ if no one can kill whales there there's no need to research the conditions of the animals there. The population will never be hunted. (You know, except for science...)
Japan is not breaking the law, but they are doing an end run around it.
cite! Law of the Sea. UN. NOAA.