Researchers studying hidden populations -- including injection drug users, men who have sex with men, & the homeless -- find that standard probability sampling methods are either inapplicable or prohibitively costly because their subjects lack a sampling frame, have privacy concerns, & constitute a small part of the general population. Therefore, researchers generally employ non-probability methods, including location sampling methods such as targeted sampling, & chain-referral methods such as snowball & respondent-driven sampling. Though nonprobability methods succeed in accessing the hidden populations, they have been insufficient for statistical inference. This paper extends the respondent-driven sampling method to show that when biases associated with chain-referral methods are analyzed in sufficient detail, a statistical theory of the sampling process can be constructed, based on which the sampling process can be redesigned to permit the derivation of indicators that are not biased & have known levels of precision. The results are based on a study of 190 injection drug users in a small Connecticut city.