Thanks for the report. I confirm the bug in Sage 8.7.beta7. 
What is strange is that ddChi seems a perfectly valid symbolic expression:
sage: ddChi = ddChi.expand(); ddChi
2*diff(chi(r, theta, phi), r)/r + cos(theta)*diff(chi(r, theta, phi), theta
)/(r^2*sin(theta)) + diff(chi(r, theta, phi), theta, theta)/r^2 + diff(chi(r
, theta, phi), phi, phi)/(r^2*sin(theta)^2) + diff(chi(r, theta, phi), r, r)
sage: (ddChi - 2*diff(chi(r, theta, phi), r)/r).simplify()
cos(theta)*diff(chi(r, theta, phi), theta)/(r^2*sin(theta)) + diff(chi(r, 
theta, phi), theta, theta)/r^2 + diff(chi(r, theta, phi), phi, phi)/(r^2*sin
(theta)^2) + diff(chi(r, theta, phi), r, r)

and yet
sage: ddChi.coefficient(diff(chi(r, theta, phi), r), 1)
0

Eric.

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