  We study Chern-Simons theories at large $N$ with either bosonic or fermionic
matter in the fundamental representation. The most fundamental operators in
these theories are mesonic line operators, the simplest example being Wilson
lines ending on fundamentals. We classify the conformal line operators along an
arbitrary smooth path as well as the spectrum of conformal dimensions and
transverse spins of their boundary operators at finite 't Hooft coupling. These
line operators are shown to satisfy first-order chiral evolution equations, in
which a smooth variation of the path is given by a factorized product of two
line operators. We argue that this equation together with the spectrum of
boundary operators are sufficient to uniquely determine the expectation values
of these operators. We demonstrate this by bootstrapping the two-point function
of the displacement operator on a straight line. We show that the line
operators in the theory of bosons and the theory of fermions satisfy the same
evolution equation and have the same spectrum of boundary operators.
