We use 3 mm multiline and continuum CARMA observations toward the first hydrostatic core (FHSC) candidate L1451-mm to characterize the envelope kinematics at 1000 au scales and investigate its evolutionary state. We detect evidence of infall and rotation in the NH2D(11,110,1), N2H+(10), and HCN(10) molecular lines. We compare the positionvelocity diagram of the NH2D(11,110,1) line with a simple kinematic model and find that it is consistent with an envelope that is both infalling and rotating while conserving angular momentum around a central mass of about 0.06 M-circle dot. The N2H+(10) LTE mass of the envelope along with the inferred infall velocity leads to a mass infall rate of approximately 6 x 10(-6) M-circle dot yr(-1), implying a young age of 10(4) years for this FHSC candidate. Assuming that the accretion onto the central object is the same as the infall rate, we obtain a minimum source size of 1.55 au, consistent with the size expected for a first core. We do not see any evidence of outflow motions or signs of outflowenvelope interaction at scales greater than or similar to 2000 au. This is consistent with previous observations that revealed a very compact outflow (less than or similar to 500 au). We conclude that L1451-mm is indeed at a very early stage of evolution, either a first core or an extremely young Class 0 protostar. Our results provide strong evidence that L1451-mm is the best candidate for being a bona fide first core.