We report observations of dense molecular gas in the star-forming galaxy EGS 13004291 (z = 1.197) using the Plateau de Bure Interferometer. We tentatively detect HCN and HNC J=2\to 1 emission when stacked together at 4σ significance, yielding line luminosities of {L}{HCN(J=2\to 1)}\prime =(9+/- 3)× {10}9 K km s‑1 pc2 and {L}{HNC(J=2\to 1)}\prime =(5+/- 2)× {10}9 K km s‑1 pc2, respectively. We also set 3σ upper limits of <7–8 ×109 K km s‑1 pc2 on the {{HCO}}+(J=2\to 1), {{{H}}}2{{O}}({3}13\to {2}20), and HC3N(J = 20 → 19) line luminosities. We serendipitously detect CO emission from two sources at z∼ 1.8 and z∼ 3.2 in the same field of view. We also detect CO(J=2\to 1) emission in EGS 13004291, showing that the excitation in the previously detected CO(J=3\to 2) line is subthermal ({r}32=0.65+/- 0.15). We find a line luminosity ratio of {L}{HCN}\prime /{L}{CO}\prime = 0.17 ± 0.07, as an indicator of the dense gas fraction. This is consistent with the median ratio observed in z> 1 galaxies ({L}{HCN}\prime /{L}{CO}\prime = 0.16 ± 0.07) and nearby ULIRGs ({L}{HCN}\prime /{L}{CO}\prime = 0.13 ± 0.03), but higher than that in local spirals ({L}{HCN}\prime /{L}{CO}\prime = 0.04 ± 0.02). Although EGS 13004291 lies significantly above the galaxy main sequence at z∼ 1, we do not find an elevated star formation efficiency (traced by {L}{FIR}/{L}{CO}\prime ) as in local starbursts, but a value consistent with main-sequence galaxies. The enhanced dense gas fraction, the subthermal gas excitation, and the lower than expected star formation efficiency of the dense molecular gas in EGS 13004291 suggest that different star formation properties may prevail in high-z starbursts. Thus, using {L}{FIR}/{L}{CO}\prime as a simple recipe to measure the star formation efficiency may be insufficient to describe the underlying mechanisms in dense star-forming environments inside the large gas reservoirs. Based on observations carried out under project ID U030 with the IRAM NOEMA Interferometer. IRAM is supported by INSU/CNRS (France), MPG (Germany), and IGN (Spain).