  Most superconductors have an isotropic, single component order parameter, and
are well described by the BCS theory for superconductivity. Unconventional,
multiple components superconductors are exceptionally rare and are much less
understood. Here, we combine scanning tunneling microscopy and angle-resolved
macroscopic transport to study the candidate chiral superconductor,
4Hb-TaS$_2$. We reveal quasi-periodic one-dimensional modulations in the
tunneling conductance accompanied by two-fold symmetric superconducting
critical field. The strong modulation of the in-plane critical field, points to
a nematic, unconventional order parameter. However, the imaged vortex core is
nearly circular symmetric, suggesting an isotropic order parameter. We
reconcile this apparent discrepancy by modeling a competition between a
dominating chiral superconducting order parameter and a nematic one, the latter
emerges close to the normal phase. Our results strongly support the existence
of two-component superconductivity in 4Hb-TaS$_2$ and can provide useful
insights to other systems with coexistent charge order and superconductivity.
