Step 1: Problem Analysis.
A 30 m tape, when used to measure 1000 m, overestimated the length by 0.10 m per tape length.
Step 2: Calculate True Length from 30m Tape.
The measured length was 1000 m. Correcting for the overestimation:
\[
1000 - 0.10 = 999.90 \, \text{m}.
\]
Step 3: Correct 20 m Chain Measurement.
The 20 m chain measured a length of 1010 m. Use the ratio of actual to measured lengths from the 30m tape to correct the 20m chain measurement:
\[
\text{Actual Length} = \left(\frac{999.90}{1000}\right) \times 1010 = 1010 \, \text{m} \times 0.9999 = 1009.899 \, \text{m}.
\]
Step 4: Conclusion.
The corrected length from the 20 m chain measurement is 1009.899 m. Therefore, there appears to be a calculation error in the original solution.
Final Answer:
\[
\boxed{1009.899 \, \text{m}}
\]