  The temperature dependence of the London penetration depth, $\lambda(T)$, was
measured in polycrystalline MgB$_2$ samples by a high-resolution, radio
frequency technique. A clear exponential temperature dependence of $\lambda(T)$
was observed at low temperature, indicating s-wave pairing. A fit to the data
gives an effective energy gap $\Delta$ of $2.8\pm0.4$ meV
($2\Delta/k_BT_c=1.7\pm0.2$), which is significantly smaller than the standard
BCS weak coupling value of 3.5. This may be explained either by an anisotropic
gap or the influence of low frequency phonon modes.
