  The growing recognition that entanglement is not exclusively a quantum
property, and does not even originate with Schr\"odinger's famous remark about
it [Proc. Camb. Phil. Soc. 31, 555 (1935)], prompts examination of its role in
marking the quantum-classical boundary. We have done this by subjecting
correlations of classical optical fields to new Bell-analysis experiments, and
report here values of the Bell parameter greater than ${\cal B} = 2.54$. This
is many standard deviations outside the limit ${\cal B} = 2$ established by the
Clauser-Horne-Shimony-Holt (CHSH) Bell inequality [Phys. Rev. Lett. 23, 880
(1969)], in agreement with our theoretical classical prediction, and not far
from the Tsirelson limit ${\cal B} = 2.828...$. These results cast a new light
on the standard quantum-classical boundary description, and suggest a
reinterpretation of it.
