We report the first look at extragalactic Cepheid variables with the James Webb Space Telescope (JWST), obtained from an archival observation of NGC 1365, host of SNIa 2012fr, a calibration path used to measure the Hubble constant. As expected, the high-resolution observations with NIRCam through F200W show better source separation from line-of-sight companions than Hubble Space Telescope (HST) images at similar near-infrared wavelengths, the spectral region that has been used to mitigate the impact of host dust on distance measurements. Using the standard star P330E as a zero-point and point-spread function reference, we photometered 31 previously known Cepheids in the JWST field, spanning
1.15
<
log
P
<
1.75
including 24 Cepheids in the longer-period interval of
1.35
<
log
P
<
1.75
. We compared the resultant period–luminosity (P-L) relations to that of 49 Cepheids in the full period range including 38 in the longer-period range observed with WFC3/IR on HST and transformed to the JWST photometric system (F200W, Vega). The P-L relations measured are in good agreement, with intercepts (at
log
P
=
1
) of 25.74 ± 0.04 and 25.72 ± 0.05 for HST and JWST, respectively. Our baseline result comes from the longer-period, higher signal-to-noise ratio Cepheids where we find 25.75 ± 0.05 and 25.75 ± 0.06 mag for HST and JWST, respectively. We find good consistency between this first JWST measurement and HST, and no evidence that HST Cepheid photometry is “biased bright” at the ∼0.2 mag level needed to mitigate the Hubble tension, though comparisons from more SN hosts are warranted and anticipated. We expect future optimized JWST observations to surpass these in quality.