We describe the construction of a highly reliable sample of ~7000 optically faint periodic variable stars with light curves obtained by the asteroid survey LINEAR across 10,000 deg^2 of the northern sky. The majority of these variables have not been cataloged yet. The sample flux limit is several magnitudes fainter than most other wide-angle surveys; the photometric errors range from ~0.03 mag at r = 15 to ~0.20 mag at r = 18. Light curves include on average 250 data points, collected over about 25 million objects, we selected ~200,000 most probable candidate variables with r