We report on simultaneous sub-second optical and X-ray timing observations of the low mass X-ray binary black hole candidate MAXI J1820+070. The bright 2018 outburst rise allowed simultaneous photometry in five optical bands ($ugriz_s$) with HiPERCAM/GTC (Optical) at frame rates over 100 Hz, together with NICER/ISS observations (X-rays). Intense (factor of two) red flaring activity in the optical is seen over a broad range of timescales down to $∼$10 ms. Cross-correlating the bands reveals a prominent anti-correlation on timescales of $∼$seconds, and a narrow sub-second correlation at a lag of $≈$+165 ms (optical lagging X-rays). This lag increases with optical wavelength, and is approximately constant over Fourier frequencies of $∼$0.3-10 Hz. These features are consistent with an origin in the inner accretion flow and jet base within $∼$5000 Gravitational radii. An additional $∼$+5 s lag feature may be ascribable to disc reprocessing. MAXI J1820+070 is the third black hole transient to display a clear $∼$0.1s optical lag, which may be common feature in such objects. The sub-second lag $variation$ with wavelength is novel, and may allow constraints on internal shock jet stratification models.