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Linear Feedback Shift Registers (LFSRs) are used as building blocks for many stream ciphers, wherein, an n-degree primitive connection polynomial is used as a feedback function to realize an n-bit LFSR. This paper shows that such LFSRs are susceptible to power analysis based Side Channel Attacks (SCA). The major contribution of this paper is the observation that the state of an n-bit LFSR can be determined by making O(n) power measurements. Interestingly, neither the primitive polynomial nor the value of n be known to the adversary launching the proposed attack. The paper also proposes a simple countermeasure for the SCA that uses n additional flipflops.