We present new FLAMES+GIRAFFE spectroscopy of 36 member stars in the isolated Local Group dwarf spheroidal galaxy Tucana. We measure a systemic velocity for the system of $vTuc$=216.7$\mathrm{<mrow\; data-mjx-texclass="ORD">-2.8</mrow><mrow\; data-mjx-texclass="ORD">+2.9</mrow>}$ km s$\mathrm{<mrow\; data-mjx-texclass="ORD">-1</mrow>}$, and a velocity dispersion of σ=14.4$\mathrm{<mrow\; data-mjx-texclass="ORD">-2.3</mrow><mrow\; data-mjx-texclass="ORD">+2.8</mrow>}$ km s$\mathrm{<mrow\; data-mjx-texclass="ORD">-1</mrow>}$. We also detect a rotation gradient of $dvrd\chi$=7.6$\mathrm{<mrow\; data-mjx-texclass="ORD">-4.3</mrow><mrow\; data-mjx-texclass="ORD">+4.2</mrow>}$ km s$\mathrm{<mrow\; data-mjx-texclass="ORD">-1</mrow>}$ kpc$\mathrm{<mrow\; data-mjx-texclass="ORD">-1</mrow>}$, which reduces the systemic velocity to $vTuc$=215.2$\mathrm{<mrow\; data-mjx-texclass="ORD">-2.7</mrow><mrow\; data-mjx-texclass="ORD">+2.8</mrow>}$ km s$\mathrm{<mrow\; data-mjx-texclass="ORD">-1</mrow>}$ and the velocity dispersion to σ=13.3$\mathrm{<mrow\; data-mjx-texclass="ORD">-2.3</mrow><mrow\; data-mjx-texclass="ORD">+2.7</mrow>}$ km s$\mathrm{<mrow\; data-mjx-texclass="ORD">-1</mrow>}$. We perform Jeans modelling of the density profile of Tucana, using the line-of-sight velocities of the member stars. We find that it favours a high central density consistent with ‘pristine’ subhaloes in Λ cold dark matter, and a massive dark matter halo (~10$\mathrm{<mrow\; data-mjx-texclass="ORD">10</mrow>}$ M$\odot$) consistent with expectations from abundance matching. Tucana appears to be significantly more centrally dense than other isolated Local Group dwarfs, making it an ideal laboratory for testing dark matter models.