The emerging marketplace for online free services in which service providers earn revenue from using consumer data in direct and indirect ways has lead to significant privacy concerns. This leads to the following question: can the online marketplace sustain multiple service providers (SPs) that offer privacy-differentiated free services? This paper studies the problem of market segmentation for the free online services market by augmenting the classical Hotelling model for market segmentation analysis to include the fact that for the free services market, a consumer values service not in monetized terms but by its quality of service (QoS) and that the differentiator of services is not product price but the privacy risk advertised by a SP. Building upon the Hotelling model, this paper presents a parametrized model for SP profit and consumer valuation of service for both the two- and multi-SP problems to show that: (i) when consumers place a high value on privacy, it leads to a lower use of private data by SPs (i.e., their advertised privacy risk reduces), and thus, SPs compete on the QoS; (ii) SPs that are capable of differentiating on services that do not directly target consumers gain larger market share; and (iii) a higher valuation of privacy by consumers forces SPs with smaller untargeted revenue to offer lower privacy risk to attract more consumers. The work also illustrates the market segmentation problem for more than two SPs and highlights the instability of such markets.