We report the first direct detection of a strong , 5 kG magnetic field on the surface of an active brown dwarf .
LSR J1835+3259 is an M8.5 dwarf exhibiting transient radio and optical emission bursts modulated by fast rotation .
We have detected the surface magnetic field as circularly polarized signatures in the 819 nm sodium lines when an active emission region faced the Earth .
Modeling Stokes profiles of these lines reveals the effective temperature of 2800 K and log gravity acceleration of 4.5 .
These parameters place LSR J1835+3259 on evolutionary tracks as a young brown dwarf with the mass of 55 \pm 4 M _ { J } and age of 22 \pm 4 Myr .
Its magnetic field is at least 5.1 kG and covers at least 11 % of the visible hemisphere .
The active region topology recovered using line profile inversions comprises hot plasma loops with a vertical stratification of optical and radio emission sources .
These loops rotate with the dwarf in and out of view causing periodic emission bursts .
The magnetic field is detected at the base of the loops .
This is the first time that we can quantitatively associate brown dwarf non-thermal bursts with a strong , 5 kG surface magnetic field and solve the puzzle of their driving mechanism .
This is also the coolest known dwarf with such a strong surface magnetic field .
The young age of LSR J1835+3259 implies that it may still maintain a disk , which may facilitate bursts via magnetospheric accretion , like in higher-mass T Tau-type stars .
Our results pave a path toward magnetic studies of brown dwarfs and hot Jupiters .