Chronicle is, in essence, another superhero origin story, but its characters feel more realistic than we usually get in such tales, as do their reactions to their new powers.
After three teenage boys in Seattle find a glowing artifact in a cave, they develop telekinesis. Being fairly average kids, their first thoughts are not of battling evil or saving the world; instead, they use their power for pranks and fun.
As the boys explore their powers, they become inseparable friends, which is a new experience for Andrew, who's always been a misfit; even as a senior, he's still the primary target of his school's bullies. Throw in a dying mother and an abusive drunken father, and it's not surprising that Andrew has a lot of barely repressed anger at the world. Andrew also has the strongest telekinetic gift of the three, and it's not long before that anger is no longer quite so repressed.
The movie is filmed in "found footage" style -- Andrew carries a video camera with him everywhere he goes -- which can often get really annoying, with all the jittery hand-held camera work, but director Josh Trank finds a clever way around that. As Andrew's powers grow, he simply floats the camera wherever he wants it, which allows it to be more stable (and even to provide tracking/dolly shots).
The movie does a very good job of mixing its special effects with its low-budget look, and the characters are better written and more rounded than you'd expect from this sort of movie; I especially appreciated the fact that the quarterback/class president/popular kid is, for a change, not an asshole, but the nicest one of the group. Performances from the cast of relative unknowns are consistently good.
There's a bit of a fumble in the last twenty minutes or so, when the movie suddenly goes overboard on the CGI effects and loses track of its subtle character development, but as a whole, it's very much worth seeing.