  Recently there has been interest in the correlation between R(D*) and the
branching ratio (BR) of $B_c \to \tau \nu$ in models with a charged scalar
H^\pm. Any enhancement of R(D*) by $H^\pm$ alone (in order to agree with
current data) also enhances $BR(B_c \to \tau \nu$), for which there has been no
direct search at hadron colliders. We show that LEP data taken at the Z peak
requires BR($B_c \to \tau \nu$) < 10%, and this constraint is significantly
stronger than the recent constraint BR($B_c \to \tau \nu$) < 30% from
considering the lifetime of B_c. In order to respect this new constraint, any
explanation of the R(D) and R(D*) anomaly in terms of $H^\pm$ alone would
require the future measurements of R(D*) to be even closer to the Standard
Model prediction. A stronger limit on BR($B_c \to \tau \nu$) (or its first
measurement) would be obtained if the L3 collaboration used all its data taken
at the Z peak.
