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 $sim$10 ms. Cross-correlating the bands reveals a prominent anti-correlation on timescales of $sim$seconds, and a narrow sub-second correlation at a lag of $approx$+165 ms (optical lagging X-rays). This lag increases with optical wavelength, and is approximately constant over Fourier frequencies of $sim$0.3-10 Hz. These features are consistent with an origin in the inner accretion flow and jet base within $sim$5000 Gravitational radii. An additional $sim$+5 s lag feature may be ascribable to disc reprocessing. MAXI J1820+070 is the third black hole transient to display a clear $sim$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.
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