We study a very basic open problem regarding the PCP characterization of NP, namely, the power of PCPs with 3 non-adaptive queries and perfect completeness. The lowest soundness known till now for such a PCP is 6/8 + ε given by a construction of Håstad . However, Zwick  shows that a 3-query non-adaptive PCP with perfect completeness cannot achieve soundness below 5/8. In this paper, we construct a 3-query non-adaptive PCP with perfect completeness and soundness 20/27 + ε, which improves upon the previous best soundness of 6/8 + ε. A standard reduction from PCPs to constraint satisfaction problems (CSPs) implies that it is NP-hard to tell if a boolean CSP on 3-variables has a satisfying assignment or no assignment satisfies more than 20/27 + ε fraction of the constraints. Our construction uses "biased Long Codes" introduced by Dinur and Safra . We develop new 3-query tests to check consistency between such codes. These tests are analyzed by extending Håstad's Fourier methods  to the biased case.