  We report penetration depth and resistivity measurements on the heavy fermion
superconductor CeCoIn_5 using a self resonant tank circuit based on a tunnel
diode oscillator. For magnetic fields applied near parallel to the
\emph{ab}-planes and temperatures below 250 mK, two phase transitions were
found. The lower field transition, within the superconducting state, is of a
second order and we identify it as the transition from the ordinary vortex
state to the Fulde, Ferrell, Larkin, Ovchinnikov (FFLO) state. The higher field
transition marks the change from the FFLO to the normal state. This higher
field transition, $H_{c2}$, is of first order up to 900 mK, the highest
temperature measured. Our normal state resistivity measurements at temperatures
between 100 and 900 mK suggest that the FFLO state is related to the change of
the quasi-particle interaction strength, $F^a_0$. Our critical field data for
different orientations and temperatures is in good agreement with recent
specific heat, magnetization, and resistivity results.
